Location: California

I am in California and have a 12 lease that is completed to an end in June. When it expires it goes month to month. The issue is that it states in the lease we must give a two months notice of moving out. I assume that is invalid though if we switch to a month to month as we are paying monthly and can move out anytime. I don't know if this is truly the case or if we are going to have to eat a month of rent and not live here. I'm no legal expert obviously but that just makes legal sense to me, though common sense is not always what the law goes by.