My lease states :
This month to month lease is to expire on April 1, or be renewed at that time. Landlord and tenant has the right to 60 day written notice to vacate.

My question is we did not hear from our landlord until I called him on April 30th to meet to give my notice to vacate. Can I vacate on may 31 with out owing June rent?

NO, either one of you have to give the 60 day notice as required in the terms of the lease. The terms of the lease except that you may get out of lease with notice. And/or they may raise rates with notice, the other terms, would still apply.

If you wanted out, you need to have your 60 days notice.