2 month to 2 month lease

[Matt Liu]

If a lease says between landlord and tenant, "We agree to the following: to give two months advance notice to monthly rent paying date, of intention to terminate tenancy"

Does that mean that if the landlord wants to terminate tenancy, she must give notice on April 30th/May1st for tenant to be gone by July 1st? Or do standard month-to-month rules apply to the landlord's whims? And does the landlord have to abstain from collecting any rent during that whole 2 month time, if the former?