Do I Have to Sign a Lease?

Your lease is up; they can kick you out at any time (provided they give proper notice, usually 30 days) without reason, just as you can pick up and move. What makes you think you would be able to rent a newly renovated apartment for the same price as your "war-zone" apartment? This is a very small increase to your rent for moving into what is basically a brand-new apartment. Either move into a new one and sign the lease, or give notice and move out completely. You and the landlord are no longer obligated to one another.