The lease is the primary document that governs how you can terminate your lease. Generally, landlords require 30 days written notice before you vacate the premises. But if your lease has not expired, given 30 days notice may not protect you from owing rent or other damages for breach of the lease. If both you and the landlord have lost your lease agreement and cannot 'remember' when your lease ends or how you should give notice to terminate you can negotiate a new agreement that would supersede the lease should they 'find' it after you move out. While you can proceed on your own, I would consult with counsel to discuss the details and possibly draft a termination agreement that protects you when you move out.
This response is for general purposes only and does not create an attorney-client relationship.