As per question, there seems to be some issue with application logic rather than thread sync.
1) If you are filling the map with static data for all the available values, and fetching the values for specific user, then it should not be dependent on the thread.
2) If there are user specific data to be dynamically loaded into the map for each request, then if you are using the same key, then the values will be overridden. If this is case, then you should change the way, the keys are mapped.
Please do post more about the problem if the issue is not clear.