diff --git a/src/_pytest/pathlib.py b/src/_pytest/pathlib.py
index c5a411b59..a12d2d6f4 100644
--- a/src/_pytest/pathlib.py
+++ b/src/_pytest/pathlib.py
@@ -357,8 +357,10 @@ def make_numbered_dir_with_cleanup(
     for i in range(10):
         try:
             p = make_numbered_dir(root, prefix, mode)
-            lock_path = create_cleanup_lock(p)
-            register_cleanup_lock_removal(lock_path)
+            # Do not lock the current dir when keep is 0
+            if keep != 0:
+                lock_path = create_cleanup_lock(p)
+                register_cleanup_lock_removal(lock_path)
         except Exception as exc:
             e = exc
         else:
diff --git a/src/_pytest/tmpdir.py b/src/_pytest/tmpdir.py
index db41b3c64..fc454be7a 100644
--- a/src/_pytest/tmpdir.py
+++ b/src/_pytest/tmpdir.py
@@ -154,10 +154,13 @@ class TempPathFactory:
                         )
                     if (rootdir_stat.st_mode & 0o077) != 0:
                         os.chmod(rootdir, rootdir_stat.st_mode & ~0o077)
+            keep = self._retention_count
+            if self._retention_policy == "none":
+                keep = 0
             basetemp = make_numbered_dir_with_cleanup(
                 prefix="pytest-",
                 root=rootdir,
-                keep=self._retention_count,
+                keep=keep,
                 lock_timeout=LOCK_TIMEOUT,
                 mode=0o700,
             )