diff --git a/clang-tools-extra/clangd/support/Threading.h b/clang-tools-extra/clangd/support/Threading.h
--- a/clang-tools-extra/clangd/support/Threading.h
+++ b/clang-tools-extra/clangd/support/Threading.h
@@ -110,12 +110,13 @@
   void wait() const { (void)wait(Deadline::infinity()); }
   LLVM_NODISCARD bool wait(Deadline D) const;
   // The name is used for tracing and debugging (e.g. to name a spawned thread).
-  void runAsync(const llvm::Twine &Name, llvm::unique_function<void()> Action);
+  void runAsync(const llvm::Twine &Name,
+                llvm::unique_function<void()> Action) const;
 
 private:
   mutable std::mutex Mutex;
   mutable std::condition_variable TasksReachedZero;
-  std::size_t InFlightTasks = 0;
+  mutable std::size_t InFlightTasks = 0;
 };
 
 /// Runs \p Action asynchronously with a new std::thread. The context will be
diff --git a/clang-tools-extra/clangd/support/Threading.cpp b/clang-tools-extra/clangd/support/Threading.cpp
--- a/clang-tools-extra/clangd/support/Threading.cpp
+++ b/clang-tools-extra/clangd/support/Threading.cpp
@@ -70,7 +70,7 @@
 }
 
 void AsyncTaskRunner::runAsync(const llvm::Twine &Name,
-                               llvm::unique_function<void()> Action) {
+                               llvm::unique_function<void()> Action) const {
   {
     std::lock_guard<std::mutex> Lock(Mutex);
     ++InFlightTasks;