What you have is a term lease for 12 months. Not a month to month lease. For term leases, you would simply vacate the premises on the last day of the lease, if you don't wish to hold over. You don't have to notify the landlord 30 days in advance if you intend to move out by July 9. But if you hold over beyond July 9 and you pay rent for the next month accepted by the landlord, you'd become become a month-to-month tenant. Then all the rules for month-to-month tenancy would apply.
So the short answer to your question. If you don't want any hassle, simply vacate by July 9. Does it say anywhere in the lease you're required to give notice of termination?