While a lease may contain a provision that requires it to be signed by both parties to be valid, and a lease must normally be signed by the party against whom enforcement is sought, that changes once the tenancy begins. If the tenant signs the lease, absent something to the contrary within the lease, the lease is binding on the tenant. If the parties negotiate a lease and start a tenancy, but for some reason do not sign the lease but the tenancy nonetheless commences, it is likely that a court will regard the lease as reflecting the terms of the tenancy.
If there is no lease that includes the provision that the landlord is claiming as a basis for early termination, then it's not "bluffing" to indicate that there is no such provision in the lease.Quoting hr for me

