First, change your user name. NEVER use your name or email address as a user name on a public internet forum. You're asking for trouble.
You can always "break" the lease, but the question will be, what are the repercussions. That might include the LL not returning part or all of the security deposit, or the LL could start a court proceeding to recover the rent for the rest of the lease.
Oh the other hand, you could go after the LL for not returning the deposit.
A lease is a contract with rights and obligations on both sides, so you would need some level of proof that the LL is ignoring the making of repairs, and that they rise to the level beyond the cosmetic. You would need record of complaints you made to the LL, complaints to the city, violations and so on. That the LL prevented the LL from completing the repair, well you would need some sort of expert to show what they were doing was merely superficial.
The warranty of habitability is not automatic. If you get to court, well it depends on many factors if a judge would agree with your defense over the landlord's claims.
Yes, perhaps you can work it out with the LL before anyone goes to court. That's always preferable, but it would likely take some degree of compromise on both sides. If you're willing to forego the deposit, then you're really talking about just one month.
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