Covered more cases and added a test

src/EditorFeatures/CSharpTest/QualifyMemberAccess/QualifyMemberAccessTests.cs

@@ -840,6 +840,25 @@ void Method2(Func<object> LocalFunction)
 CodeStyleOptions.QualifyMethodAccess);
         }
 
+        [WorkItem(38043, "https://github.com/dotnet/roslyn/issues/38043")]
+        [Fact, Trait(Traits.Feature, Traits.Features.CodeActionsQualifyMemberAccess)]
+        public async Task QualifyLocalMethodAccess_NotSuggestedInCollectionInitializer()
+        {
+            await TestMissingAsyncWithOption(
+@"using System;
+using System.Collections.Generic;
+
+class C
+{
+    void Method()
+    {
+        object LocalFunction() => new object();
+        var dict = new Dictionary<Func<object>, int>() { { [|LocalFunction|], 1 } };
+    }
+}",
+CodeStyleOptions.QualifyMethodAccess);
+        }
+
         [WorkItem(7065, "https://github.com/dotnet/roslyn/issues/7065")]
         [Fact(Skip = "https://github.com/dotnet/roslyn/issues/7587"), Trait(Traits.Feature, Traits.Features.CodeActionsQualifyMemberAccess)]
         public async Task QualifyEventAccess_EventSubscription()

src/Features/Core/Portable/QualifyMemberAccess/AbstractQualifyMemberAccessDiagnosticAnalyzer.cs

@@ -108,7 +108,7 @@ private void AnalyzeOperation(OperationAnalysisContext context, IOperation opera
 
             // if we can't find a member then we can't do anything.  Also, we shouldn't qualify
             // accesses to static members.  
-            if (IsStaticMemberOrTargetMethod(operation))
+            if (IsMemberOrTargetMethodStaticOrLocalFunction(operation))
             {
                 return;
             }
@@ -147,15 +147,16 @@ private void AnalyzeOperation(OperationAnalysisContext context, IOperation opera
             }
         }
 
-        private bool IsStaticMemberOrTargetMethod(IOperation operation)
+        private bool IsMemberOrTargetMethodStaticOrLocalFunction(IOperation operation)
         {
             switch (operation)
             {
                 case IMemberReferenceOperation memberReferenceOperation:
                     return memberReferenceOperation.Member == null || memberReferenceOperation.Member.IsStatic ||
-                        memberReferenceOperation.Member is IMethodSymbol method && method.MethodKind == MethodKind.LocalFunction;
+                        memberReferenceOperation.Member is IMethodSymbol memberMethod && memberMethod.MethodKind == MethodKind.LocalFunction;
                 case IInvocationOperation invocationOperation:
-                    return invocationOperation.TargetMethod == null || invocationOperation.TargetMethod.IsStatic;
+                    return invocationOperation.TargetMethod == null || invocationOperation.TargetMethod.IsStatic ||
+                        invocationOperation.TargetMethod is IMethodSymbol targetMethod && targetMethod.MethodKind == MethodKind.LocalFunction;
                 default:
                     throw ExceptionUtilities.UnexpectedValue(operation);
             }