I have a 2001 Toyota Corolla. Would 15x8 rims with a +10mm offset and a 3 inch lip fit?

If the wheels don't fit without offset, forget it. Your car uses 14 inch wheels. If you go to 15, you will need a lower profile tire. Corollas are low cars for aerodynamics and handling improvement, though they could use some tightening up. Maybe you can make the larger wheel work on your car with enlarged fenders but don't pit "Fat Mary in the back seat, and if the tire snags your fender while tirning, it will throw you off course and tear the fender up. Unless the wheels you want are particularly stylish and you need to have that "look", it's a waste of money.