Simple LRU cache with an expiration time
I still don't see how it is LRU, but that's beside the point.

One obvious problem is a race between testing for cache.get(key).isExpired() and cache.remove(key) on the next line. It is very well possible for another thread to preempt right in between just to get() that object.

A thread performing get() would believe that it updated useTime, yet the entry would have been removed.

Depending on the use case, the consequences could be catastrophic, or harmless.