Why is the power to three bathrooms' lights out?
Let's think about the bathroom wiring rules for a second.  The latest Code says you use one of two methods for the 20A circuit that must be dedicated to bathroom receptacles. 


In one case, a circuit can power receptacles in any number of bathrooms, but only bathroom receptacles, not  fixed loads in the bathroom such as lights. 
In the other case, a circuit can power receptacles in one bathroom only, but can also power fixed loads like lights in that same bathroom.  This is a weaker design since if you trip the bathroom breaker, the lights go out.  


It sounds like your builder used method #1, with a twist, he put in a second circuit right alongside that powered each bathroom's lights. 

No breakers are tripped, OK.  In modern construction they are fond of a connection method on switches called "backstabs", where the wire is jabbed into a hole on the back.  These are prone to failure, and it is the first place I would look.  Putting the wires properly around the side screws is the far more reliable way.  

Any wiring failure in a chain from the panel is either at the failing location, or at the last working location prior.  I would expect to find it in the nearest bathroom to the panel.