To answer your question on the lights in your bath (why they still work): Well, the bathroom receptacles are on a separate circuit from the bath lights.
How old is your home? Newer homes have Bath GFI's that are
placed in one of the bathrooms in the house. You mention your outside receptacle is dead--along with the bath. It could very well be an outside GFCI. I would go with Ron's suggestion, and get back to us. Please list age of home.