RE2 resets the cache when it reaches a (configurable) size limit. Which I found out the hard way when I had to debug almost-periodic latency spikes in a service I managed, where a very inefficient regex caused linear growth in the Lazy DFA, until it hit the limit, then all threads had to wait for its reset for a few hundred milliseconds, and then it all started again.
I'm not sure if dropping the whole cache is the only feasible mitigation, or some gradual pruning would also be possible.
Either way, if you cannot assume that your cache grows monotonically, synchronization becomes more complicated: the trick mentioned in the other comment about only locking the slow path may not be applicable anymore. RE2 uses RW-locking for this.