Always add the store to lifespan_manager then let the store implement…

…ation decides to handle to close or not

litestar/app.py

@@ -393,8 +393,7 @@ def __init__(
         )
         self._lifespan_managers = config.lifespan
         for store in self.stores._stores.values():
-            if store.handle_client_shutdown:
-                self._lifespan_managers.append(store)
+            self._lifespan_managers.append(store)
         self._server_lifespan_managers = [p.server_lifespan for p in config.plugins or [] if isinstance(p, CLIPlugin)]
         self.experimental_features = frozenset(config.experimental_features or [])
         self.get_logger: GetLogger = get_logger_placeholder

litestar/stores/redis.py

@@ -72,7 +72,8 @@ def __init__(
         )
 
     async def _shutdown(self) -> None:
-        await self._redis.aclose(close_connection_pool=True)
+        if self.handle_client_shutdown:
+            await self._redis.aclose(close_connection_pool=True)
 
     async def __aexit__(
         self,