Monthly Lease Inside New York City: 30 days of notice. The 30-day notice is most commonly used to terminate a month-to-month lease, but it can also be used to change the lease.Be aware that if you are in a monthtomonth tenancy, the landlord or tenant must only give 30 days' notice before the lease ends. A tenant must inform the landlord of the name of any occupant within. According to Texas law, landlords must return the deposit within 30 days of lease termination, minus any deductions for damages or unpaid rent.