So is there a time restriction on pool use?
The only thing you may run into is pool maintenance/chemical testing - oh, and ducks impeding DD's laps! Seriously - if there's an issue with the pool, they'll have the "No Swimming" signs up with the area blocked off. The same thing will happen if there is lightning in the area.

I assume there will not be lifeguards that early.
Correct - there will not be pool attendants on duty at that time of the morning.