If your lease specifies the terms and conditions how the lease i

and the tenant did not comply with all the terms and conditions, the landlord can use the terms provided in the lease to notify the tenant to terminate the lease. (I am not sure what is in your lease on termination a lease, or to deny a renewal).

If the tenant did not comply with the terms to renew the lease, AND the landlord did not follow the terms to refuse the renewal, then the lease automatically becomes month to month starting from the first 1st of the month after the original term expires.

A month-to-month lease can be terminated by serving a 30 day notification(to avoid problem, follow the service procedure correctly). You do not have to pay them extra to get them moving.