You will not be bound by the lease if they never sign it. However, you should not sign a lease that does not contain all the terms of your agreement and just take her word for it. If she is unwilling to put it in the lease she is going to screw you over, most likely. At this point you are apparently still in the premises so you are month to month. To get out now you will have to give the notice of intent to vacate provided in the original lease. But you also have to worry about the issue you raisse with respect to them retroactively signing the lease you wanted her to sign once you have left. Thererore, I think you should send a certified letter to the landlord which: a) recounts the events surrounding the attempted execution of a new lease and ask them to confirm that no new lease has been executed within 5 days of their receipt of the letter and that you are on a month to month tenancy at this point and that if you do not hear from them within those 5 days you will take that as a sign that no lease was executed; and b) gives them the required 30 or 60 days notice of your intent to vacate the month to month tenancy in the event no lease is in effect. Hopefully this covers you on all fronts. But it means you are probably stuck with the premises until at least the endo of December and possibly the end of January at this point if your lease requires 60 days notice. Good luck.
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Generally, if the manager or landlord have already signed the new lease without making any additional changes, they may be able to claim you are bound by that lease. If they have not yet signed the lease, you should be able to give written notice that you have changed your mind and no longer agree to the new lease. If you are not sure whether or not they have signed the lease or if they will claim they have signed the lease, you may want to give the manager written notice that if she does not immediately provide you with a signed copy of the new lease, you will assume it has not been signed and your agreement to the new lease is withdrawn.
This answer is offered as a public service for general information only and should not be relied upon as legal advice.