Index: clang/lib/Format/TokenAnnotator.cpp
===================================================================
--- clang/lib/Format/TokenAnnotator.cpp
+++ clang/lib/Format/TokenAnnotator.cpp
@@ -40,6 +40,24 @@
   return Tok.Tok.getIdentifierInfo() != nullptr;
 }
 
+/// With `Left` being '(', check if we're at either `[...](` or
+/// `...]<...>(`.
+static bool isLambdaParameterList(const FormatToken *Left) {
+  if (!Left->Previous)
+    return false;
+
+  // Skip <...> if present.
+  if (Left->Previous && Left->Previous->is(tok::greater) &&
+      Left->Previous->MatchingParen &&
+      Left->Previous->MatchingParen->is(TT_TemplateOpener))
+    Left = Left->Previous->MatchingParen;
+
+  // Check for `[...](`.
+  return Left->Previous && Left->Previous->is(tok::r_square) &&
+         Left->Previous->MatchingParen &&
+         Left->Previous->MatchingParen->is(TT_LambdaLSquare);
+}
+
 /// A parser that gathers additional information about tokens.
 ///
 /// The \c TokenAnnotator tries to match parenthesis and square brakets and
@@ -191,9 +209,7 @@
                Left->Previous->is(TT_JsTypeColon)) {
       // let x: (SomeType);
       Contexts.back().IsExpression = false;
-    } else if (Left->Previous && Left->Previous->is(tok::r_square) &&
-               Left->Previous->MatchingParen &&
-               Left->Previous->MatchingParen->is(TT_LambdaLSquare)) {
+    } else if (isLambdaParameterList(Left)) {
       // This is a parameter list of a lambda expression.
       Contexts.back().IsExpression = false;
     } else if (Line.InPPDirective &&
Index: clang/lib/Format/UnwrappedLineParser.cpp
===================================================================
--- clang/lib/Format/UnwrappedLineParser.cpp
+++ clang/lib/Format/UnwrappedLineParser.cpp
@@ -1440,8 +1440,11 @@
     case tok::identifier:
     case tok::numeric_constant:
     case tok::coloncolon:
+    case tok::kw_class:
     case tok::kw_mutable:
     case tok::kw_noexcept:
+    case tok::kw_template:
+    case tok::kw_typename:
       nextToken();
       break;
     // Specialization of a template with an integer parameter can contain
Index: clang/unittests/Format/FormatTest.cpp
===================================================================
--- clang/unittests/Format/FormatTest.cpp
+++ clang/unittests/Format/FormatTest.cpp
@@ -12888,6 +12888,10 @@
                "  return 1; //\n"
                "};");
 
+  // Lambdas with explicit template argument lists.
+  verifyFormat(
+      "auto L = []<template <typename> class T, class U>(T<U> &&a) {};\n");
+
   // Multiple lambdas in the same parentheses change indentation rules. These
   // lambdas are forced to start on new lines.
   verifyFormat("SomeFunction(\n"
@@ -12905,8 +12909,8 @@
                "    },\n"
                "    1);\n");
 
-  // A multi-line lambda passed as arg1 forces arg0 to be pushed out, just like the arg0
-  // case above.
+  // A multi-line lambda passed as arg1 forces arg0 to be pushed out, just like
+  // the arg0 case above.
   auto Style = getGoogleStyle();
   Style.BinPackArguments = false;
   verifyFormat("SomeFunction(\n"