Thank you. Unless there was a clause in the lease which required a 60 day notice, you have no legal obligation to provide them. The purpose behind a lease, is so the parties know when it will end. If they did not ask about renewal nor did you, then it would be known that you will vacate at the end of the lease. I have provided below the Florida Statute below and a section of it, so you can see what the landlord is required to do, to even impose a claim and if they failed to do so, they have no legal right to keep your deposit.
(a) Upon the vacating of the premises for termination of the lease, if the landlord does not intend to impose a claim on the security deposit, the landlord shall have 15 days to return the security deposit together with interest if otherwise required, or the landlord shall have 30 days to give the tenant written notice by certified mail to the tenant’s last known mailing address of his or her intention to impose a claim on the deposit and the reason for imposing the claim. The notice shall contain a statement in substantially the following form:
This is a notice of my intention to impose a claim for damages in the amount of upon your security deposit, due to . It is sent to you as required by s. 83.49(3), Florida Statutes. You are hereby notified that you must object in writing to this deduction from your security deposit within 15 days from the time you receive this notice or I will be authorized to deduct my claim from your security deposit. Your objection must be sent to (landlord’s address) .
If the landlord fails to give the required notice within the 30-day period, he or she forfeits the right to impose a claim upon the security deposit and may not seek a setoff against the deposit but may file an action for damages after return of the deposit.
(b) Unless the tenant objects to the imposition of the landlord’s claim or the amount thereof within 15 days after receipt of the landlord’s notice of intention to impose a claim, the landlord may then deduct the amount of his or her claim and shall remit the balance of the deposit to the tenant within 30 days after the date of the notice of intention to impose a claim for damages. The failure of the tenant to make a timely objection does not waive any rights of the tenant to seek damages in a separate action. http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&URL=0000-0099/0083/Sections/0083.49.html