diff --git a/libcxx/docs/Status/RangesAlgorithms.csv b/libcxx/docs/Status/RangesAlgorithms.csv
--- a/libcxx/docs/Status/RangesAlgorithms.csv
+++ b/libcxx/docs/Status/RangesAlgorithms.csv
@@ -9,7 +9,7 @@
 Search,adjacent_find,Nikolas Klauser,`D126610 <https://llvm.org/D126610>`_,✅
 Search,mismatch,Nikolas Klauser,`D117817 <https://llvm.org/D117817>`_,✅
 Search,equal,Nikolas Klauser,`D123681 <https://llvm.org/D123681>`_,✅
-Search,lexicographical_compare,Nikolas Klauser,`D127130 <https://llvm.org/D127130>`_,Under review
+Search,lexicographical_compare,Nikolas Klauser,`D127130 <https://llvm.org/D127130>`_,✅
 Search,partition_point,Christopher Di Bella,`D105794 <https://llvm.org/D105794>`_,Under review
 Search,lower_bound,Nikolas Klauser,`D121964 <https://llvm.org/D121964>`_,✅
 Search,upper_bound,Nikolas Klauser,`D121964 <https://llvm.org/D121964>`_,✅
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -89,6 +89,7 @@
   __algorithm/ranges_is_partitioned.h
   __algorithm/ranges_is_sorted.h
   __algorithm/ranges_is_sorted_until.h
+  __algorithm/ranges_lexicographical_compare.h
   __algorithm/ranges_lower_bound.h
   __algorithm/ranges_max.h
   __algorithm/ranges_max_element.h
diff --git a/libcxx/include/__algorithm/ranges_lexicographical_compare.h b/libcxx/include/__algorithm/ranges_lexicographical_compare.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_lexicographical_compare.h
@@ -0,0 +1,98 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_LEXICOGRAPHICAL_COMPARE_H
+#define _LIBCPP___ALGORITHM_RANGES_LEXICOGRAPHICAL_COMPARE_H
+
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/projected.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __lexicographical_compare {
+struct __fn {
+
+  template <class _Iter1, class _Sent1, class _Iter2, class _Sent2, class _Proj1, class _Proj2, class _Comp>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  bool __lexicographical_compare_impl(_Iter1 __first1, _Sent1 __last1,
+                                      _Iter2 __first2, _Sent2 __last2,
+                                      _Comp& __comp,
+                                      _Proj1& __proj1,
+                                      _Proj2& __proj2) {
+    while (__first2 != __last2) {
+      if (__first1 == __last1
+       || std::invoke(__comp, std::invoke(__proj1, *__first1), std::invoke(__proj2, *__first2)))
+        return true;
+      if (std::invoke(__comp, std::invoke(__proj2, *__first2), std::invoke(__proj1, *__first1)))
+        return false;
+      ++__first1;
+      ++__first2;
+    }
+    return false;
+  }
+
+  template <input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
+            input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
+            class _Proj1 = identity,
+            class _Proj2 = identity,
+            indirect_strict_weak_order<projected<_Iter1, _Proj1>, projected<_Iter2, _Proj2>> _Comp = ranges::less>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  bool operator()(_Iter1 __first1, _Sent1 __last1,
+                  _Iter2 __first2, _Sent2 __last2,
+                  _Comp __comp = {},
+                  _Proj1 __proj1 = {},
+                  _Proj2 __proj2 = {}) const {
+    return __lexicographical_compare_impl(std::move(__first1), std::move(__last1),
+                                          std::move(__first2), std::move(__last2),
+                                          __comp,
+                                          __proj1,
+                                          __proj2);
+  }
+
+  template <input_range _Range1,
+            input_range _Range2,
+            class _Proj1 = identity,
+            class _Proj2 = identity,
+            indirect_strict_weak_order<projected<iterator_t<_Range1>, _Proj1>,
+                                       projected<iterator_t<_Range2>, _Proj2>> _Comp = ranges::less>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  bool operator()(_Range1&& __range1, _Range2&& __range2, _Comp __comp = {}, _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const {
+    return __lexicographical_compare_impl(ranges::begin(__range1), ranges::end(__range1),
+                                          ranges::begin(__range2), ranges::end(__range2),
+                                          __comp,
+                                          __proj1,
+                                          __proj2);
+  }
+
+};
+} // namespace __lexicographical_compare
+
+inline namespace __cpo {
+  inline constexpr auto lexicographical_compare = __lexicographical_compare::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_LEXICOGRAPHICAL_COMPARE_H
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -424,6 +424,22 @@
     constexpr borrowed_iterator_t<R>
       ranges::replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});                     // since C++20
 
+  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
+           class Proj1 = identity, class Proj2 = identity,
+           indirect_strict_weak_order<projected<I1, Proj1>,
+                                      projected<I2, Proj2>> Comp = ranges::less>
+    constexpr bool
+      ranges::lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
+                                      Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});    // since C++20
+
+  template<input_range R1, input_range R2, class Proj1 = identity,
+           class Proj2 = identity,
+           indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
+                                      projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
+    constexpr bool
+      ranges::lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
+                                      Proj1 proj1 = {}, Proj2 proj2 = {});                    // since C++20
+
 }
 
     constexpr bool     // constexpr in C++20
@@ -1161,6 +1177,7 @@
 #include <__algorithm/ranges_is_partitioned.h>
 #include <__algorithm/ranges_is_sorted.h>
 #include <__algorithm/ranges_is_sorted_until.h>
+#include <__algorithm/ranges_lexicographical_compare.h>
 #include <__algorithm/ranges_lower_bound.h>
 #include <__algorithm/ranges_max.h>
 #include <__algorithm/ranges_max_element.h>
diff --git a/libcxx/include/module.modulemap.in b/libcxx/include/module.modulemap.in
--- a/libcxx/include/module.modulemap.in
+++ b/libcxx/include/module.modulemap.in
@@ -238,144 +238,145 @@
     export *
 
     module __algorithm {
-      module adjacent_find            { private header "__algorithm/adjacent_find.h" }
-      module all_of                   { private header "__algorithm/all_of.h" }
-      module any_of                   { private header "__algorithm/any_of.h" }
-      module binary_search            { private header "__algorithm/binary_search.h" }
-      module clamp                    { private header "__algorithm/clamp.h" }
-      module comp                     { private header "__algorithm/comp.h" }
-      module comp_ref_type            { private header "__algorithm/comp_ref_type.h" }
-      module copy                     { private header "__algorithm/copy.h" }
-      module copy_backward            { private header "__algorithm/copy_backward.h" }
-      module copy_if                  { private header "__algorithm/copy_if.h" }
-      module copy_n                   { private header "__algorithm/copy_n.h" }
-      module count                    { private header "__algorithm/count.h" }
-      module count_if                 { private header "__algorithm/count_if.h" }
-      module equal                    { private header "__algorithm/equal.h" }
-      module equal_range              { private header "__algorithm/equal_range.h" }
-      module fill                     { private header "__algorithm/fill.h" }
-      module fill_n                   { private header "__algorithm/fill_n.h" }
-      module find                     { private header "__algorithm/find.h" }
-      module find_end                 { private header "__algorithm/find_end.h" }
-      module find_first_of            { private header "__algorithm/find_first_of.h" }
-      module find_if                  { private header "__algorithm/find_if.h" }
-      module find_if_not              { private header "__algorithm/find_if_not.h" }
-      module for_each                 { private header "__algorithm/for_each.h" }
-      module for_each_n               { private header "__algorithm/for_each_n.h" }
-      module generate                 { private header "__algorithm/generate.h" }
-      module generate_n               { private header "__algorithm/generate_n.h" }
-      module half_positive            { private header "__algorithm/half_positive.h" }
-      module in_found_result          { private header "__algorithm/in_found_result.h" }
-      module in_fun_result            { private header "__algorithm/in_fun_result.h" }
-      module in_in_out_result         { private header "__algorithm/in_in_out_result.h" }
-      module in_in_result             { private header "__algorithm/in_in_result.h" }
-      module in_out_out_result        { private header "__algorithm/in_out_out_result.h" }
-      module in_out_result            { private header "__algorithm/in_out_result.h" }
-      module includes                 { private header "__algorithm/includes.h" }
-      module inplace_merge            { private header "__algorithm/inplace_merge.h" }
-      module is_heap                  { private header "__algorithm/is_heap.h" }
-      module is_heap_until            { private header "__algorithm/is_heap_until.h" }
-      module is_partitioned           { private header "__algorithm/is_partitioned.h" }
-      module is_permutation           { private header "__algorithm/is_permutation.h" }
-      module is_sorted                { private header "__algorithm/is_sorted.h" }
-      module is_sorted_until          { private header "__algorithm/is_sorted_until.h" }
-      module iter_swap                { private header "__algorithm/iter_swap.h" }
-      module iterator_operations      { private header "__algorithm/iterator_operations.h" }
-      module lexicographical_compare  { private header "__algorithm/lexicographical_compare.h" }
-      module lower_bound              { private header "__algorithm/lower_bound.h" }
-      module make_heap                { private header "__algorithm/make_heap.h" }
-      module max                      { private header "__algorithm/max.h" }
-      module max_element              { private header "__algorithm/max_element.h" }
-      module merge                    { private header "__algorithm/merge.h" }
-      module min                      { private header "__algorithm/min.h" }
-      module min_element              { private header "__algorithm/min_element.h" }
-      module min_max_result           { private header "__algorithm/min_max_result.h" }
-      module minmax                   { private header "__algorithm/minmax.h" }
-      module minmax_element           { private header "__algorithm/minmax_element.h" }
-      module mismatch                 { private header "__algorithm/mismatch.h" }
-      module move                     { private header "__algorithm/move.h" }
-      module move_backward            { private header "__algorithm/move_backward.h" }
-      module next_permutation         { private header "__algorithm/next_permutation.h" }
-      module none_of                  { private header "__algorithm/none_of.h" }
-      module nth_element              { private header "__algorithm/nth_element.h" }
-      module partial_sort             { private header "__algorithm/partial_sort.h" }
-      module partial_sort_copy        { private header "__algorithm/partial_sort_copy.h" }
-      module partition                { private header "__algorithm/partition.h" }
-      module partition_copy           { private header "__algorithm/partition_copy.h" }
-      module partition_point          { private header "__algorithm/partition_point.h" }
-      module pop_heap                 { private header "__algorithm/pop_heap.h" }
-      module prev_permutation         { private header "__algorithm/prev_permutation.h" }
-      module push_heap                { private header "__algorithm/push_heap.h" }
-      module ranges_adjacent_find     { private header "__algorithm/ranges_adjacent_find.h" }
-      module ranges_all_of            { private header "__algorithm/ranges_all_of.h" }
-      module ranges_any_of            { private header "__algorithm/ranges_any_of.h" }
-      module ranges_binary_search     { private header "__algorithm/ranges_binary_search.h" }
-      module ranges_copy              { private header "__algorithm/ranges_copy.h" }
-      module ranges_copy_backward     { private header "__algorithm/ranges_copy_backward.h" }
-      module ranges_copy_if           { private header "__algorithm/ranges_copy_if.h" }
-      module ranges_copy_n            { private header "__algorithm/ranges_copy_n.h" }
-      module ranges_count             { private header "__algorithm/ranges_count.h" }
-      module ranges_count_if          { private header "__algorithm/ranges_count_if.h" }
-      module ranges_equal             { private header "__algorithm/ranges_equal.h" }
-      module ranges_fill              { private header "__algorithm/ranges_fill.h" }
-      module ranges_fill_n            { private header "__algorithm/ranges_fill_n.h" }
-      module ranges_find              { private header "__algorithm/ranges_find.h" }
-      module ranges_find_first_of     { private header "__algorithm/ranges_find_first_of.h" }
-      module ranges_find_if           { private header "__algorithm/ranges_find_if.h" }
-      module ranges_find_if_not       { private header "__algorithm/ranges_find_if_not.h" }
-      module ranges_for_each          { private header "__algorithm/ranges_for_each.h" }
-      module ranges_for_each_n        { private header "__algorithm/ranges_for_each_n.h" }
-      module ranges_is_partitioned    { private header "__algorithm/ranges_is_partitioned.h" }
-      module ranges_is_sorted         { private header "__algorithm/ranges_is_sorted.h" }
-      module ranges_is_sorted_until   { private header "__algorithm/ranges_is_sorted_until.h" }
-      module ranges_lower_bound       { private header "__algorithm/ranges_lower_bound.h" }
-      module ranges_max               { private header "__algorithm/ranges_max.h" }
-      module ranges_max_element       { private header "__algorithm/ranges_max_element.h" }
-      module ranges_min               { private header "__algorithm/ranges_min.h" }
-      module ranges_min_element       { private header "__algorithm/ranges_min_element.h" }
-      module ranges_minmax            { private header "__algorithm/ranges_minmax.h" }
-      module ranges_minmax_element    { private header "__algorithm/ranges_minmax_element.h" }
-      module ranges_mismatch          { private header "__algorithm/ranges_mismatch.h" }
-      module ranges_none_of           { private header "__algorithm/ranges_none_of.h" }
-      module ranges_replace           { private header "__algorithm/ranges_replace.h" }
-      module ranges_replace_if        { private header "__algorithm/ranges_replace_if.h" }
-      module ranges_reverse           { private header "__algorithm/ranges_reverse.h" }
-      module ranges_swap_ranges       { private header "__algorithm/ranges_swap_ranges.h" }
-      module ranges_transform         { private header "__algorithm/ranges_transform.h" }
-      module ranges_upper_bound       { private header "__algorithm/ranges_upper_bound.h" }
-      module remove                   { private header "__algorithm/remove.h" }
-      module remove_copy              { private header "__algorithm/remove_copy.h" }
-      module remove_copy_if           { private header "__algorithm/remove_copy_if.h" }
-      module remove_if                { private header "__algorithm/remove_if.h" }
-      module replace                  { private header "__algorithm/replace.h" }
-      module replace_copy             { private header "__algorithm/replace_copy.h" }
-      module replace_copy_if          { private header "__algorithm/replace_copy_if.h" }
-      module replace_if               { private header "__algorithm/replace_if.h" }
-      module reverse                  { private header "__algorithm/reverse.h" }
-      module reverse_copy             { private header "__algorithm/reverse_copy.h" }
-      module rotate                   { private header "__algorithm/rotate.h" }
-      module rotate_copy              { private header "__algorithm/rotate_copy.h" }
-      module sample                   { private header "__algorithm/sample.h" }
-      module search                   { private header "__algorithm/search.h" }
-      module search_n                 { private header "__algorithm/search_n.h" }
-      module set_difference           { private header "__algorithm/set_difference.h" }
-      module set_intersection         { private header "__algorithm/set_intersection.h" }
-      module set_symmetric_difference { private header "__algorithm/set_symmetric_difference.h" }
-      module set_union                { private header "__algorithm/set_union.h" }
-      module shift_left               { private header "__algorithm/shift_left.h" }
-      module shift_right              { private header "__algorithm/shift_right.h" }
-      module shuffle                  { private header "__algorithm/shuffle.h" }
-      module sift_down                { private header "__algorithm/sift_down.h" }
-      module sort                     { private header "__algorithm/sort.h" }
-      module sort_heap                { private header "__algorithm/sort_heap.h" }
-      module stable_partition         { private header "__algorithm/stable_partition.h" }
-      module stable_sort              { private header "__algorithm/stable_sort.h" }
-      module swap_ranges              { private header "__algorithm/swap_ranges.h" }
-      module transform                { private header "__algorithm/transform.h" }
-      module unique                   { private header "__algorithm/unique.h" }
-      module unique_copy              { private header "__algorithm/unique_copy.h" }
-      module unwrap_iter              { private header "__algorithm/unwrap_iter.h" }
-      module upper_bound              { private header "__algorithm/upper_bound.h" }
+      module adjacent_find                   { private header "__algorithm/adjacent_find.h" }
+      module all_of                          { private header "__algorithm/all_of.h" }
+      module any_of                          { private header "__algorithm/any_of.h" }
+      module binary_search                   { private header "__algorithm/binary_search.h" }
+      module clamp                           { private header "__algorithm/clamp.h" }
+      module comp                            { private header "__algorithm/comp.h" }
+      module comp_ref_type                   { private header "__algorithm/comp_ref_type.h" }
+      module copy                            { private header "__algorithm/copy.h" }
+      module copy_backward                   { private header "__algorithm/copy_backward.h" }
+      module copy_if                         { private header "__algorithm/copy_if.h" }
+      module copy_n                          { private header "__algorithm/copy_n.h" }
+      module count                           { private header "__algorithm/count.h" }
+      module count_if                        { private header "__algorithm/count_if.h" }
+      module equal                           { private header "__algorithm/equal.h" }
+      module equal_range                     { private header "__algorithm/equal_range.h" }
+      module fill                            { private header "__algorithm/fill.h" }
+      module fill_n                          { private header "__algorithm/fill_n.h" }
+      module find                            { private header "__algorithm/find.h" }
+      module find_end                        { private header "__algorithm/find_end.h" }
+      module find_first_of                   { private header "__algorithm/find_first_of.h" }
+      module find_if                         { private header "__algorithm/find_if.h" }
+      module find_if_not                     { private header "__algorithm/find_if_not.h" }
+      module for_each                        { private header "__algorithm/for_each.h" }
+      module for_each_n                      { private header "__algorithm/for_each_n.h" }
+      module generate                        { private header "__algorithm/generate.h" }
+      module generate_n                      { private header "__algorithm/generate_n.h" }
+      module half_positive                   { private header "__algorithm/half_positive.h" }
+      module in_found_result                 { private header "__algorithm/in_found_result.h" }
+      module in_fun_result                   { private header "__algorithm/in_fun_result.h" }
+      module in_in_out_result                { private header "__algorithm/in_in_out_result.h" }
+      module in_in_result                    { private header "__algorithm/in_in_result.h" }
+      module in_out_out_result               { private header "__algorithm/in_out_out_result.h" }
+      module in_out_result                   { private header "__algorithm/in_out_result.h" }
+      module includes                        { private header "__algorithm/includes.h" }
+      module inplace_merge                   { private header "__algorithm/inplace_merge.h" }
+      module is_heap                         { private header "__algorithm/is_heap.h" }
+      module is_heap_until                   { private header "__algorithm/is_heap_until.h" }
+      module is_partitioned                  { private header "__algorithm/is_partitioned.h" }
+      module is_permutation                  { private header "__algorithm/is_permutation.h" }
+      module is_sorted                       { private header "__algorithm/is_sorted.h" }
+      module is_sorted_until                 { private header "__algorithm/is_sorted_until.h" }
+      module iter_swap                       { private header "__algorithm/iter_swap.h" }
+      module iterator_operations             { private header "__algorithm/iterator_operations.h" }
+      module lexicographical_compare         { private header "__algorithm/lexicographical_compare.h" }
+      module lower_bound                     { private header "__algorithm/lower_bound.h" }
+      module make_heap                       { private header "__algorithm/make_heap.h" }
+      module max                             { private header "__algorithm/max.h" }
+      module max_element                     { private header "__algorithm/max_element.h" }
+      module merge                           { private header "__algorithm/merge.h" }
+      module min                             { private header "__algorithm/min.h" }
+      module min_element                     { private header "__algorithm/min_element.h" }
+      module min_max_result                  { private header "__algorithm/min_max_result.h" }
+      module minmax                          { private header "__algorithm/minmax.h" }
+      module minmax_element                  { private header "__algorithm/minmax_element.h" }
+      module mismatch                        { private header "__algorithm/mismatch.h" }
+      module move                            { private header "__algorithm/move.h" }
+      module move_backward                   { private header "__algorithm/move_backward.h" }
+      module next_permutation                { private header "__algorithm/next_permutation.h" }
+      module none_of                         { private header "__algorithm/none_of.h" }
+      module nth_element                     { private header "__algorithm/nth_element.h" }
+      module partial_sort                    { private header "__algorithm/partial_sort.h" }
+      module partial_sort_copy               { private header "__algorithm/partial_sort_copy.h" }
+      module partition                       { private header "__algorithm/partition.h" }
+      module partition_copy                  { private header "__algorithm/partition_copy.h" }
+      module partition_point                 { private header "__algorithm/partition_point.h" }
+      module pop_heap                        { private header "__algorithm/pop_heap.h" }
+      module prev_permutation                { private header "__algorithm/prev_permutation.h" }
+      module push_heap                       { private header "__algorithm/push_heap.h" }
+      module ranges_adjacent_find            { private header "__algorithm/ranges_adjacent_find.h" }
+      module ranges_all_of                   { private header "__algorithm/ranges_all_of.h" }
+      module ranges_any_of                   { private header "__algorithm/ranges_any_of.h" }
+      module ranges_binary_search            { private header "__algorithm/ranges_binary_search.h" }
+      module ranges_copy                     { private header "__algorithm/ranges_copy.h" }
+      module ranges_copy_backward            { private header "__algorithm/ranges_copy_backward.h" }
+      module ranges_copy_if                  { private header "__algorithm/ranges_copy_if.h" }
+      module ranges_copy_n                   { private header "__algorithm/ranges_copy_n.h" }
+      module ranges_count                    { private header "__algorithm/ranges_count.h" }
+      module ranges_count_if                 { private header "__algorithm/ranges_count_if.h" }
+      module ranges_equal                    { private header "__algorithm/ranges_equal.h" }
+      module ranges_fill                     { private header "__algorithm/ranges_fill.h" }
+      module ranges_fill_n                   { private header "__algorithm/ranges_fill_n.h" }
+      module ranges_find                     { private header "__algorithm/ranges_find.h" }
+      module ranges_find_first_of            { private header "__algorithm/ranges_find_first_of.h" }
+      module ranges_find_if                  { private header "__algorithm/ranges_find_if.h" }
+      module ranges_find_if_not              { private header "__algorithm/ranges_find_if_not.h" }
+      module ranges_for_each                 { private header "__algorithm/ranges_for_each.h" }
+      module ranges_for_each_n               { private header "__algorithm/ranges_for_each_n.h" }
+      module ranges_is_partitioned           { private header "__algorithm/ranges_is_partitioned.h" }
+      module ranges_is_sorted                { private header "__algorithm/ranges_is_sorted.h" }
+      module ranges_is_sorted_until          { private header "__algorithm/ranges_is_sorted_until.h" }
+      module ranges_lexicographical_compare  { private header "__algorithm/ranges_lexicographical_compare.h" }
+      module ranges_lower_bound              { private header "__algorithm/ranges_lower_bound.h" }
+      module ranges_max                      { private header "__algorithm/ranges_max.h" }
+      module ranges_max_element              { private header "__algorithm/ranges_max_element.h" }
+      module ranges_min                      { private header "__algorithm/ranges_min.h" }
+      module ranges_min_element              { private header "__algorithm/ranges_min_element.h" }
+      module ranges_minmax                   { private header "__algorithm/ranges_minmax.h" }
+      module ranges_minmax_element           { private header "__algorithm/ranges_minmax_element.h" }
+      module ranges_mismatch                 { private header "__algorithm/ranges_mismatch.h" }
+      module ranges_none_of                  { private header "__algorithm/ranges_none_of.h" }
+      module ranges_replace                  { private header "__algorithm/ranges_replace.h" }
+      module ranges_replace_if               { private header "__algorithm/ranges_replace_if.h" }
+      module ranges_reverse                  { private header "__algorithm/ranges_reverse.h" }
+      module ranges_swap_ranges              { private header "__algorithm/ranges_swap_ranges.h" }
+      module ranges_transform                { private header "__algorithm/ranges_transform.h" }
+      module ranges_upper_bound              { private header "__algorithm/ranges_upper_bound.h" }
+      module remove                          { private header "__algorithm/remove.h" }
+      module remove_copy                     { private header "__algorithm/remove_copy.h" }
+      module remove_copy_if                  { private header "__algorithm/remove_copy_if.h" }
+      module remove_if                       { private header "__algorithm/remove_if.h" }
+      module replace                         { private header "__algorithm/replace.h" }
+      module replace_copy                    { private header "__algorithm/replace_copy.h" }
+      module replace_copy_if                 { private header "__algorithm/replace_copy_if.h" }
+      module replace_if                      { private header "__algorithm/replace_if.h" }
+      module reverse                         { private header "__algorithm/reverse.h" }
+      module reverse_copy                    { private header "__algorithm/reverse_copy.h" }
+      module rotate                          { private header "__algorithm/rotate.h" }
+      module rotate_copy                     { private header "__algorithm/rotate_copy.h" }
+      module sample                          { private header "__algorithm/sample.h" }
+      module search                          { private header "__algorithm/search.h" }
+      module search_n                        { private header "__algorithm/search_n.h" }
+      module set_difference                  { private header "__algorithm/set_difference.h" }
+      module set_intersection                { private header "__algorithm/set_intersection.h" }
+      module set_symmetric_difference        { private header "__algorithm/set_symmetric_difference.h" }
+      module set_union                       { private header "__algorithm/set_union.h" }
+      module shift_left                      { private header "__algorithm/shift_left.h" }
+      module shift_right                     { private header "__algorithm/shift_right.h" }
+      module shuffle                         { private header "__algorithm/shuffle.h" }
+      module sift_down                       { private header "__algorithm/sift_down.h" }
+      module sort                            { private header "__algorithm/sort.h" }
+      module sort_heap                       { private header "__algorithm/sort_heap.h" }
+      module stable_partition                { private header "__algorithm/stable_partition.h" }
+      module stable_sort                     { private header "__algorithm/stable_sort.h" }
+      module swap_ranges                     { private header "__algorithm/swap_ranges.h" }
+      module transform                       { private header "__algorithm/transform.h" }
+      module unique                          { private header "__algorithm/unique.h" }
+      module unique_copy                     { private header "__algorithm/unique_copy.h" }
+      module unwrap_iter                     { private header "__algorithm/unwrap_iter.h" }
+      module upper_bound                     { private header "__algorithm/upper_bound.h" }
     }
   }
   module any {
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
@@ -140,8 +140,8 @@
     (void)std::ranges::is_sorted_until(a, Less(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::inplace_merge(first, mid, last, Less(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::inplace_merge(a, mid, Less(&copies)); assert(copies == 0); }
-    //(void)std::ranges::lexicographical_compare(first, last, first2, last2, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::lexicographical_compare(a, b, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::lexicographical_compare(first, last, first2, last2, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::lexicographical_compare(a, b, Less(&copies)); assert(copies == 0);
     (void)std::ranges::lower_bound(first, last, value, Less(&copies)); assert(copies == 0);
     (void)std::ranges::lower_bound(a, value, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::make_heap(first, last, Less(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
@@ -123,8 +123,8 @@
     (void)std::ranges::is_sorted_until(a, Less(), Proj(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::inplace_merge(first, mid, last, Less(), Proj(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::inplace_merge(a, mid, Less(), Proj(&copies)); assert(copies == 0); }
-    //(void)std::ranges::lexicographical_compare(first, last, first2, last2, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::lexicographical_compare(a, b, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::lexicographical_compare(first, last, first2, last2, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::lexicographical_compare(a, b, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::lower_bound(first, last, value, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::lower_bound(a, value, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::make_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/private_headers.verify.cpp b/libcxx/test/libcxx/private_headers.verify.cpp
--- a/libcxx/test/libcxx/private_headers.verify.cpp
+++ b/libcxx/test/libcxx/private_headers.verify.cpp
@@ -126,6 +126,7 @@
 #include <__algorithm/ranges_is_partitioned.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_is_partitioned.h'}}
 #include <__algorithm/ranges_is_sorted.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_is_sorted.h'}}
 #include <__algorithm/ranges_is_sorted_until.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_is_sorted_until.h'}}
+#include <__algorithm/ranges_lexicographical_compare.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_lexicographical_compare.h'}}
 #include <__algorithm/ranges_lower_bound.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_lower_bound.h'}}
 #include <__algorithm/ranges_max.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_max.h'}}
 #include <__algorithm/ranges_max_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_max_element.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.lex.comparison/ranges.lexicographical_compare.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.lex.comparison/ranges.lexicographical_compare.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.lex.comparison/ranges.lexicographical_compare.pass.cpp
@@ -0,0 +1,243 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
+//          class Proj1 = identity, class Proj2 = identity,
+//          indirect_strict_weak_order<projected<I1, Proj1>,
+//                                     projected<I2, Proj2>> Comp = ranges::less>
+//   constexpr bool
+//     ranges::lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
+//                                     Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
+// template<input_range R1, input_range R2, class Proj1 = identity,
+//          class Proj2 = identity,
+//          indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
+//                                     projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
+//   constexpr bool
+//     ranges::lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
+//                                     Proj1 proj1 = {}, Proj2 proj2 = {});
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+template <class Iter1, class Sent1 = Iter1, class Iter2 = int*, class Sent2 = int*>
+concept HasLexicographicalCompareIt = requires(Iter1 first1, Sent1 last1, Iter2 first2, Sent2 last2) {
+  std::ranges::lexicographical_compare(first1, last1, first2, last2);
+};
+
+template <class Range1, class Range2 = UncheckedRange<int*>>
+concept HasLexicographicalCompareR = requires(Range1 range1, Range2 range2) {
+  std::ranges::lexicographical_compare(range1, range2);
+};
+
+static_assert(HasLexicographicalCompareIt<int*>);
+static_assert(!HasLexicographicalCompareIt<InputIteratorNotDerivedFrom>);
+static_assert(!HasLexicographicalCompareIt<InputIteratorNotIndirectlyReadable>);
+static_assert(!HasLexicographicalCompareIt<InputIteratorNotInputOrOutputIterator>);
+static_assert(!HasLexicographicalCompareIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasLexicographicalCompareIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, InputIteratorNotDerivedFrom>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, InputIteratorNotIndirectlyReadable>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, InputIteratorNotInputOrOutputIterator>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, int*, SentinelForNotSemiregular>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasLexicographicalCompareIt<int*, int*, int**, int**>); // not indirect_strict_weak_order
+
+static_assert(HasLexicographicalCompareR<UncheckedRange<int*>>);
+static_assert(!HasLexicographicalCompareR<InputRangeNotDerivedFrom>);
+static_assert(!HasLexicographicalCompareR<InputRangeNotIndirectlyReadable>);
+static_assert(!HasLexicographicalCompareR<InputRangeNotInputOrOutputIterator>);
+static_assert(!HasLexicographicalCompareR<InputRangeNotSentinelSemiregular>);
+static_assert(!HasLexicographicalCompareR<InputRangeNotSentinelEqualityComparableWith>);
+static_assert(!HasLexicographicalCompareR<UncheckedRange<int*>, InputRangeNotDerivedFrom>);
+static_assert(!HasLexicographicalCompareR<UncheckedRange<int*>, InputRangeNotIndirectlyReadable>);
+static_assert(!HasLexicographicalCompareR<UncheckedRange<int*>, InputRangeNotInputOrOutputIterator>);
+static_assert(!HasLexicographicalCompareR<UncheckedRange<int*>, InputRangeNotSentinelSemiregular>);
+static_assert(!HasLexicographicalCompareR<UncheckedRange<int*>, InputRangeNotSentinelEqualityComparableWith>);
+static_assert(!HasLexicographicalCompareIt<UncheckedRange<int*>, UncheckedRange<int**>>); // not indirect_strict_weak_order
+
+template <int N, int M>
+struct Data {
+  std::array<int, N> input1;
+  std::array<int, M> input2;
+  bool expected;
+};
+
+template <class Iter1, class Sent1, class Iter2, class Sent2, int N, int M>
+constexpr void test(Data<N, M> d) {
+  {
+    std::same_as<bool> decltype(auto) ret =
+        std::ranges::lexicographical_compare(Iter1(d.input1.data()), Sent1(Iter1(d.input1.data() + d.input1.size())),
+                                             Iter2(d.input2.data()), Sent2(Iter2(d.input2.data() + d.input2.size())));
+    assert(ret == d.expected);
+  }
+  {
+    auto range1 = std::ranges::subrange(Iter1(d.input1.data()), Sent1(Iter1(d.input1.data() + d.input1.size())));
+    auto range2 = std::ranges::subrange(Iter2(d.input2.data()), Sent2(Iter2(d.input2.data() + d.input2.size())));
+    std::same_as<bool> decltype(auto) ret =
+        std::ranges::lexicographical_compare(range1, range2);
+    assert(ret == d.expected);
+  }
+}
+
+template <class Iter1, class Sent1, class Iter2, class Sent2 = Iter2>
+constexpr void test_iterators() {
+  // simple test
+  test<Iter1, Sent1, Iter2, Sent2, 4, 4>({.input1 = {1, 2}, .input2 = {1, 2, 3, 4}, .expected = true});
+  // ranges are identical
+  test<Iter1, Sent1, Iter2, Sent2, 4, 4>({.input1 = {1, 2, 3, 4}, .input2 = {1, 2, 3, 4}, .expected = false});
+  // first range is empty
+  test<Iter1, Sent1, Iter2, Sent2, 0, 4>({.input1 = {}, .input2 = {1, 2, 3, 4}, .expected = true});
+  // second range is empty
+  test<Iter1, Sent1, Iter2, Sent2, 4, 0>({.input1 = {1, 2, 3, 4}, .input2 = {}, .expected = false});
+  // both ranges are empty
+  test<Iter1, Sent1, Iter2, Sent2, 0, 0>({.input1 = {}, .input2 = {}, .expected = false});
+  // the first range compares less; first range is smaller
+  test<Iter1, Sent1, Iter2, Sent2, 3, 5>({.input1 = {1, 2, 3}, .input2 = {1, 2, 4, 5, 6}, .expected = true});
+  // the second range compares less; first range is smaller
+  test<Iter1, Sent1, Iter2, Sent2, 3, 5>({.input1 = {1, 2, 4}, .input2 = {1, 2, 3, 4, 5}, .expected = false});
+  // the first range compares less; second range is smaller
+  test<Iter1, Sent1, Iter2, Sent2, 5, 3>({.input1 = {1, 2, 3, 4, 5}, .input2 = {1, 2, 4}, .expected = true});
+  // the second range compares less; second range is smaller
+  test<Iter1, Sent1, Iter2, Sent2, 5, 3>({.input1 = {1, 2, 4, 5, 6}, .input2 = {1, 2, 3}, .expected = false});
+}
+
+template <class Iter1, class Sent1 = Iter1>
+constexpr void test_iterators2() {
+  test_iterators<Iter1, Sent1, cpp17_input_iterator<int*>, sentinel_wrapper<cpp17_input_iterator<int*>>>();
+  test_iterators<Iter1, Sent1, cpp20_input_iterator<int*>, sentinel_wrapper<cpp20_input_iterator<int*>>>();
+  test_iterators<Iter1, Sent1, forward_iterator<int*>>();
+  test_iterators<Iter1, Sent1, bidirectional_iterator<int*>>();
+  test_iterators<Iter1, Sent1, random_access_iterator<int*>>();
+  test_iterators<Iter1, Sent1, contiguous_iterator<int*>>();
+  test_iterators<Iter1, Sent1, int*>();
+  test_iterators<Iter1, Sent1, const int*>();
+}
+
+constexpr bool test() {
+  test_iterators2<cpp17_input_iterator<int*>, sentinel_wrapper<cpp17_input_iterator<int*>>>();
+  test_iterators2<cpp20_input_iterator<int*>, sentinel_wrapper<cpp20_input_iterator<int*>>>();
+  test_iterators2<forward_iterator<int*>>();
+  test_iterators2<bidirectional_iterator<int*>>();
+  test_iterators2<random_access_iterator<int*>>();
+  test_iterators2<contiguous_iterator<int*>>();
+  test_iterators2<int*>();
+  test_iterators2<const int*>();
+
+  { // check that custom projections and the comparator are used properly
+    {
+      int a[] = {3, 4, 5, 6};
+      int b[] = {24, 33, 42, 51};
+
+      auto ret = std::ranges::lexicographical_compare(std::begin(a), std::end(a),
+                                                      std::begin(b), std::end(b),
+                                                      [](int lhs, int rhs) { return lhs == rhs + 5; },
+                                                      [](int v) { return v - 2; },
+                                                      [](int v) { return v / 3; });
+      assert(!ret);
+    }
+    {
+      int a[] = {3, 4, 5, 6};
+      int b[] = {24, 33, 42, 51};
+
+      auto ret = std::ranges::lexicographical_compare(a, b,
+                                                      [](int lhs, int rhs) { return lhs == rhs + 5; },
+                                                      [](int v) { return v - 2; },
+                                                      [](int v) { return v / 3; });
+      assert(!ret);
+    }
+  }
+
+  { // check that std::invoke is used
+    struct S {
+      constexpr S(int i_) : i(i_) {}
+      constexpr bool compare(const S& j) const { return j.i < i; }
+      constexpr const S& identity() const { return *this; }
+      int i;
+    };
+    {
+      S a[] = {1, 2, 3, 4};
+      auto ret = std::ranges::lexicographical_compare(std::begin(a), std::end(a),
+                                                      std::begin(a), std::end(a),
+                                                      &S::compare,
+                                                      &S::identity,
+                                                      &S::identity);
+      assert(!ret);
+    }
+    {
+      S a[] = {1, 2, 3, 4};
+      auto ret = std::ranges::lexicographical_compare(a, a, &S::compare, &S::identity, &S::identity);
+      assert(!ret);
+    }
+  }
+
+  { // check that the implicit conversion to bool works
+    {
+      int a[] = {1, 2, 3, 4};
+      auto ret = std::ranges::lexicographical_compare(std::begin(a), std::end(a),
+                                                      std::begin(a), std::end(a),
+                                                      [](int i, int j) { return BooleanTestable{i < j}; });
+      assert(!ret);
+    }
+    {
+      int a[] = {1, 2, 3, 4};
+      auto ret = std::ranges::lexicographical_compare(a, a, [](int i, int j) { return BooleanTestable{i < j}; });
+      assert(!ret);
+    }
+  }
+
+  { // check that the complexity requirements are met
+    {
+      int predCount = 0;
+      auto pred = [&](int i, int j) { ++predCount; return i < j; };
+      auto proj1Count = 0;
+      auto proj1 = [&](int i) { ++proj1Count; return i; };
+      auto proj2Count = 0;
+      auto proj2 = [&](int i) { ++proj2Count; return i; };
+      int a[] = {1, 2, 3, 4, 5};
+      auto ret = std::ranges::lexicographical_compare(std::begin(a), std::end(a), std::begin(a), std::end(a), pred, proj1, proj2);
+      assert(!ret);
+      assert(predCount == 10);
+      assert(proj1Count == 10);
+      assert(proj2Count == 10);
+    }
+    {
+      int predCount = 0;
+      auto pred = [&](int i, int j) { ++predCount; return i < j; };
+      auto proj1Count = 0;
+      auto proj1 = [&](int i) { ++proj1Count; return i; };
+      auto proj2Count = 0;
+      auto proj2 = [&](int i) { ++proj2Count; return i; };
+      int a[] = {1, 2, 3, 4, 5};
+      auto ret = std::ranges::lexicographical_compare(a, a, pred, proj1, proj2);
+      assert(!ret);
+      assert(predCount == 10);
+      assert(proj1Count == 10);
+      assert(proj2Count == 10);
+    }
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
--- a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
+++ b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
@@ -93,7 +93,7 @@
 //static_assert(test(std::ranges::is_permutation, a, a));
 static_assert(test(std::ranges::is_sorted, a));
 static_assert(test(std::ranges::is_sorted_until, a));
-//static_assert(test(std::ranges::lexicographical_compare, a, a));
+static_assert(test(std::ranges::lexicographical_compare, a, a));
 static_assert(test(std::ranges::lower_bound, a, 42));
 //static_assert(test(std::ranges::make_heap, a));
 static_assert(test(std::ranges::max, a));
diff --git a/libcxx/test/support/boolean_testable.h b/libcxx/test/support/boolean_testable.h
--- a/libcxx/test/support/boolean_testable.h
+++ b/libcxx/test/support/boolean_testable.h
@@ -9,6 +9,8 @@
 #ifndef LIBCXX_TEST_SUPPORT_BOOLEAN_TESTABLE_H
 #define LIBCXX_TEST_SUPPORT_BOOLEAN_TESTABLE_H
 
+#include "test_macros.h"
+
 #if TEST_STD_VER > 17
 
 class BooleanTestable {