What to add for the update portion in ConcurrentDictionary AddOrUpdate

You need to pass a Func which returns the value to be stored in the dictionary in case of an update. I guess in your case (since you don’t distinguish between add and update) this would be:

var sessionId = a.Session.SessionID.ToString();
userDic.AddOrUpdate(
  authUser.UserId,
  sessionId,
  (key, oldValue) => sessionId);

I.e. the Func always returns the sessionId, so that both Add and Update set the same value.

BTW: there is a sample on the MSDN page.