diff --git a/setup.cfg b/setup.cfg
index 64bcfd4547..b6425b6e83 100755
--- a/setup.cfg
+++ b/setup.cfg
@@ -25,7 +25,7 @@ project_urls =
 packages = find:
 install_requires =
     aiorwlock==1.1.0
-    anyio>=3.7.1,<4.5.0
+    anyio>=3.7.1
     appdirs>=1.4.4
     appdirs-stubs>=0.1.0
     async-generator>=1.10
diff --git a/src/firebolt/client/auth/base.py b/src/firebolt/client/auth/base.py
index 56af8026eb..4c4132e3c2 100644
--- a/src/firebolt/client/auth/base.py
+++ b/src/firebolt/client/auth/base.py
@@ -1,15 +1,18 @@
+import logging
 from abc import abstractmethod
 from enum import IntEnum
 from time import time
 from typing import AsyncGenerator, Generator, Optional
 
-from anyio import Lock, get_current_task
+from anyio import Lock
 from httpx import Auth as HttpxAuth
 from httpx import Request, Response, codes
 
 from firebolt.utils.token_storage import TokenSecureStorage
 from firebolt.utils.util import Timer, cached_property, get_internal_error_code
 
+logger = logging.getLogger(__name__)
+
 
 class FireboltAuthVersion(IntEnum):
     """Enum for Firebolt authentication versions."""
@@ -199,12 +202,19 @@ async def async_auth_flow(
             finally:
                 # token gets updated only after flow.send is called
                 # so unlock only after that
-                # TODO: FIR-38687 Fix support for anyio 4.5.0+
-                if (
-                    self._lock.locked()
-                    and self._lock._owner_task == get_current_task()  # type: ignore
-                ):
-                    self._lock.release()
+                self._release_lock()
+
+    def _release_lock(self) -> None:
+        """Release the lock if held."""
+        if self._lock.locked():
+            try:
+                self._lock.release()
+            except RuntimeError as e:
+                # Check the error string since RuntimeError is very generic
+                if "a Lock you don't own" not in str(e):
+                    raise
+                # This task does not own the lock, can't release
+                logging.warning("Tried to release a lock not owned by the current task")
 
     def sync_auth_flow(self, request: Request) -> Generator[Request, Response, None]:
         """