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I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
If the lease doesn't require advance notice to avoid an additional penalty, they can't charge you that. The purpose of charging someone two month's rent when they break a lease is to offset the money the landlord will lose from trying to find a new tenant. Tacking on an additional 2 months rent would amount to a penalty for breaking a contract, and the law frowns on that as a matter of public policy. They have a right to be put in the same position they'd be in if you hadn't broken the lease (meaning, they get rent until they can find a new tenant). They're not allowed to PROFIT for you breaking the lease.
You don't have to pay extra and can sue for a refund if they keep your security deposit for this reason.
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