Is it possible to update the user-defined authorizer context (i.e., event.requestContext.authorizer.context) after the initial authorizer lambda has already run?

I have a NodeJS/Websocket/API Gateway/Lambda application that is making use of the authorizer lambda's context capability (i.e., event.requestContext.authorizer.context) to store certain session data. This context data is conveniently available for every subsequent lambda invocation after (and including) the websocket's $connect event.

The problem is that some of the session data we have stored in the context will eventually become stale. Is there a way to update this authorizer context data after the authorizer has already run? I am honestly just trying to avoid unnecessary calls to DynamoDB.