diff --git a/src/mcp/server/lowlevel/server.py b/src/mcp/server/lowlevel/server.py
index 562de31b7..17d3d60d7 100644
--- a/src/mcp/server/lowlevel/server.py
+++ b/src/mcp/server/lowlevel/server.py
@@ -93,7 +93,7 @@ async def main():
 
 logger = logging.getLogger(__name__)
 
-LifespanResultT = TypeVar("LifespanResultT")
+LifespanResultT = TypeVar("LifespanResultT", default=Any)
 RequestT = TypeVar("RequestT", default=Any)
 
 # type aliases for tool call results