Index: llvm/utils/lit/lit/cl_arguments.py
===================================================================
--- llvm/utils/lit/lit/cl_arguments.py
+++ llvm/utils/lit/lit/cl_arguments.py
@@ -11,6 +11,7 @@
 class TestOrder(enum.Enum):
     DEFAULT = enum.auto()
     RANDOM = enum.auto()
+    LEXICAL = enum.auto()
 
 
 def parse_args():
@@ -150,9 +151,22 @@
             metavar="N",
             help="Maximum time to spend testing (in seconds)",
             type=_positive_int)
+    selection_group.add_argument("--default-order",
+            dest="order",
+            help="Run tests in default order",
+            action="store_const",
+            const=TestOrder.DEFAULT,
+            default=TestOrder.DEFAULT)
+    selection_group.add_argument("--lexical-order",
+            dest="order",
+            help="Run tests in lexical order",
+            action="store_const",
+            const=TestOrder.LEXICAL)
     selection_group.add_argument("--shuffle",
+            dest="order",
             help="Run tests in random order",
-            action="store_true")
+            action="store_const",
+            const=TestOrder.RANDOM)
     selection_group.add_argument("-i", "--incremental",
             help="Run failed tests first (DEPRECATED: now always enabled)",
             action="store_true")
@@ -215,11 +229,6 @@
     if opts.incremental:
         print('WARNING: --incremental is deprecated. Failing tests now always run first.')
 
-    if opts.shuffle:
-        opts.order = TestOrder.RANDOM
-    else:
-        opts.order = TestOrder.DEFAULT
-
     if opts.numShards or opts.runShard:
         if not opts.numShards or not opts.runShard:
             parser.error("--num-shards and --run-shard must be used together")
Index: llvm/utils/lit/lit/main.py
===================================================================
--- llvm/utils/lit/lit/main.py
+++ llvm/utils/lit/lit/main.py
@@ -169,6 +169,8 @@
     if order == TestOrder.RANDOM:
         import random
         random.shuffle(tests)
+    elif order == TestOrder.LEXICAL:
+        tests.sort(key=lambda t: t.getFullName())
     else:
         assert order == TestOrder.DEFAULT, 'Unknown TestOrder value'
         tests.sort(key=lambda t: (not t.previous_failure, -t.previous_elapsed, t.getFullName()))
Index: llvm/utils/lit/tests/custom-result-category.py
===================================================================
--- llvm/utils/lit/tests/custom-result-category.py
+++ llvm/utils/lit/tests/custom-result-category.py
@@ -1,9 +1,6 @@
 # UNSUPPORTED: system-windows
 # Test lit.main.add_result_category() extension API.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/custom-result-category/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 %{inputs}/custom-result-category | FileCheck %s
 
 # CHECK: CUSTOM_PASS: custom-result-category :: test1.txt
Index: llvm/utils/lit/tests/googletest-format.py
===================================================================
--- llvm/utils/lit/tests/googletest-format.py
+++ llvm/utils/lit/tests/googletest-format.py
@@ -1,8 +1,5 @@
 # Check the various features of the GoogleTest format.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/googletest-format/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -v %{inputs}/googletest-format > %t.out
 # FIXME: Temporarily dump test output so we can debug failing tests on
 # buildbots.
Index: llvm/utils/lit/tests/googletest-upstream-format.py
===================================================================
--- llvm/utils/lit/tests/googletest-upstream-format.py
+++ llvm/utils/lit/tests/googletest-upstream-format.py
@@ -1,8 +1,5 @@
 # Check the various features of the GoogleTest format.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/googletest-upstream-format/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -v %{inputs}/googletest-upstream-format > %t.out
 # RUN: FileCheck < %t.out %s
 #
Index: llvm/utils/lit/tests/lit.cfg
===================================================================
--- llvm/utils/lit/tests/lit.cfg
+++ llvm/utils/lit/tests/lit.cfg
@@ -61,7 +61,7 @@
 config.substitutions.append(('%{inputs}', os.path.join(
     config.test_source_root, 'Inputs')))
 config.substitutions.append(('%{lit}',
-    "{env} %{{python}} {lit}".format(
+    "{env} %{{python}} {lit} --lexical-order".format(
         env="env -u FILECHECK_OPTS",
         lit=os.path.join(lit_path, 'lit.py'))))
 config.substitutions.append(('%{python}', '"%s"' % (sys.executable)))
Index: llvm/utils/lit/tests/progress-bar.py
===================================================================
--- llvm/utils/lit/tests/progress-bar.py
+++ llvm/utils/lit/tests/progress-bar.py
@@ -1,8 +1,5 @@
 # Check the simple progress bar.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/progress-bar/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -s %{inputs}/progress-bar > %t.out
 # RUN: FileCheck < %t.out %s
 #
Index: llvm/utils/lit/tests/reorder.py
===================================================================
--- llvm/utils/lit/tests/reorder.py
+++ llvm/utils/lit/tests/reorder.py
@@ -1,7 +1,7 @@
 ## Check that we can reorder test runs.
 
 # RUN: cp %{inputs}/reorder/.lit_test_times.txt %{inputs}/reorder/.lit_test_times.txt.orig
-# RUN: %{lit} -j1 %{inputs}/reorder > %t.out
+# RUN: %{lit} --default-order -j1 %{inputs}/reorder > %t.out
 # RUN: cp %{inputs}/reorder/.lit_test_times.txt %{inputs}/reorder/.lit_test_times.txt.new
 # RUN: cp %{inputs}/reorder/.lit_test_times.txt.orig %{inputs}/reorder/.lit_test_times.txt
 # RUN: not diff %{inputs}/reorder/.lit_test_times.txt.new %{inputs}/reorder/.lit_test_times.txt.orig
Index: llvm/utils/lit/tests/shtest-env.py
===================================================================
--- llvm/utils/lit/tests/shtest-env.py
+++ llvm/utils/lit/tests/shtest-env.py
@@ -1,8 +1,5 @@
 # Check the env command
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-env/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -a -v %{inputs}/shtest-env \
 # RUN: | FileCheck -match-full-lines %s
 #
Index: llvm/utils/lit/tests/shtest-format.py
===================================================================
--- llvm/utils/lit/tests/shtest-format.py
+++ llvm/utils/lit/tests/shtest-format.py
@@ -1,8 +1,5 @@
 # Check the various features of the ShTest format.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-format/.lit_test_times.txt
-
 # RUN: rm -f %t.xml
 # RUN: not %{lit} -j 1 -v %{inputs}/shtest-format --xunit-xml-output %t.xml > %t.out
 # RUN: FileCheck < %t.out %s
Index: llvm/utils/lit/tests/shtest-keyword-parse-errors.py
===================================================================
--- llvm/utils/lit/tests/shtest-keyword-parse-errors.py
+++ llvm/utils/lit/tests/shtest-keyword-parse-errors.py
@@ -1,6 +1,3 @@
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-keyword-parse-errors/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -vv %{inputs}/shtest-keyword-parse-errors > %t.out
 # RUN: FileCheck -input-file %t.out %s
 #
Index: llvm/utils/lit/tests/shtest-not.py
===================================================================
--- llvm/utils/lit/tests/shtest-not.py
+++ llvm/utils/lit/tests/shtest-not.py
@@ -1,8 +1,5 @@
 # Check the not command
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-not/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -a -v %{inputs}/shtest-not \
 # RUN: | FileCheck -match-full-lines %s
 #
Index: llvm/utils/lit/tests/shtest-run-at-line.py
===================================================================
--- llvm/utils/lit/tests/shtest-run-at-line.py
+++ llvm/utils/lit/tests/shtest-run-at-line.py
@@ -1,9 +1,6 @@
 # Check that -vv makes the line number of the failing RUN command clear.
 # (-v is actually sufficient in the case of the internal shell.)
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-run-at-line/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -vv %{inputs}/shtest-run-at-line > %t.out
 # RUN: FileCheck --input-file %t.out %s
 #
Index: llvm/utils/lit/tests/shtest-shell.py
===================================================================
--- llvm/utils/lit/tests/shtest-shell.py
+++ llvm/utils/lit/tests/shtest-shell.py
@@ -1,8 +1,5 @@
 # Check the internal shell handling component of the ShTest format.
 
-# FIXME: this test depends on order of tests
-# RUN: rm -f %{inputs}/shtest-shell/.lit_test_times.txt
-
 # RUN: not %{lit} -j 1 -v %{inputs}/shtest-shell > %t.out
 # FIXME: Temporarily dump test output so we can debug failing tests on
 # buildbots.
@@ -11,8 +8,6 @@
 #
 # Test again in non-UTF shell to catch potential errors with python 2 seen
 # on stdout-encoding.txt
-# FIXME: lit's testing sets source_root == exec_root which complicates running lit more than once per test.
-# RUN: rm -f %{inputs}/shtest-shell/.lit_test_times.txt
 # RUN: env PYTHONIOENCODING=ascii not %{lit} -j 1 -a %{inputs}/shtest-shell > %t.ascii.out
 # FIXME: Temporarily dump test output so we can debug failing tests on
 # buildbots.