Index: lldb/source/Plugins/ScriptInterpreter/Python/ScriptInterpreterPython.cpp
===================================================================
--- lldb/source/Plugins/ScriptInterpreter/Python/ScriptInterpreterPython.cpp
+++ lldb/source/Plugins/ScriptInterpreter/Python/ScriptInterpreterPython.cpp
@@ -328,31 +328,45 @@
 #endif
   }
 
-  void InitializeThreadsPrivate() {
-// Since Python 3.7 `Py_Initialize` calls `PyEval_InitThreads` inside itself,
-// so there is no way to determine whether the embedded interpreter
-// was already initialized by some external code. `PyEval_ThreadsInitialized`
-// would always return `true` and `PyGILState_Ensure/Release` flow would be
-// executed instead of unlocking GIL with `PyEval_SaveThread`. When
-// an another thread calls `PyGILState_Ensure` it would get stuck in deadlock.
-#if (PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION >= 7) || (PY_MAJOR_VERSION > 3)
-    // The only case we should go further and acquire the GIL: it is unlocked.
+  /// Acquires the GIL if it hasn't already been acquired by someone else.
+  void EnsureGIL() {
+    // If this thread already holds the GIL then there is nothing to initialize
+    // or set up.
     if (PyGILState_Check())
       return;
-#endif
+    Log *log(lldb_private::GetLogIfAllCategoriesSet(LIBLLDB_LOG_SCRIPT));
+    // Acquire the GIL.
+    m_was_already_initialized = true;
+    m_gil_state = PyGILState_Ensure();
+    LLDB_LOGV(log, "Ensured PyGILState. Previous state = {0}locked\n",
+              m_gil_state == PyGILState_UNLOCKED ? "un" : "");
+  }
 
-    if (PyEval_ThreadsInitialized()) {
-      Log *log(lldb_private::GetLogIfAllCategoriesSet(LIBLLDB_LOG_SCRIPT));
+  /// Initializes Python's threading support if needed and acquires the GIL.
+  void InitializeThreadsPrivate() {
+    // With Python 3.9 PyEval_InitThreads does nothing and is marked as
+    // deprecated. With Python 3.11 the function also got removed.
+    // PyEval_InitThreads is always called from Py_Initialize/Py_InitializeEx
+    // since Python 3.7 so we don't need to call it manually.
 
-      m_was_already_initialized = true;
-      m_gil_state = PyGILState_Ensure();
-      LLDB_LOGV(log, "Ensured PyGILState. Previous state = {0}locked\n",
-                m_gil_state == PyGILState_UNLOCKED ? "un" : "");
+    // The only thing we need to do for Python>=3.7 is to acquire the GIL as
+    // that's we promised the caller of this function.
+#if (PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION >= 7) || (PY_MAJOR_VERSION > 3)
+    EnsureGIL();
+#else
+    // For Python<3.7 call PyEval_InitThreads if this hasn't already done
+    // before by someone else (as indicated by PyEval_ThreadsInitialized).
+    // Manually try to take the GIL so that we fulfill our contract with the
+    // caller in case threading support has already been initialized.
+    if (PyEval_ThreadsInitialized()) {
+      EnsureGIL();
       return;
     }
 
-    // InitThreads acquires the GIL if it hasn't been called before.
+    // InitThreads acquires the GIL if it hasn't been called before so no
+    // need to manually acquire it.
     PyEval_InitThreads();
+#endif
   }
 
   TerminalState m_stdin_tty_state;