First, there does not have to be 2 signed copies for your residential lease to be valid. One copy, executed (signed) by both parties is enough to create a valid, enforceable contract. If you move out, without providing notice required under the lease, then the landlord could sue you under the residential contract. The landlord may have trouble producing the original but they'll likely have a photocopy and this will be sufficient in court.
There are reasons that would allow for you to move out of the apartment without the threat of a lawsuit. First, if there is something significantly wrong with the apartment itself. For example, if there is a rat infestation or a bug problem that is so severe the apartment is inhabitable. A few bugs or mice won't be enough, you'll need to show some kind of large infestation. Or, if the residence is inhabitable because the water pipes have burst, the air conditioning creates a constant leak, the roofing is collapsing. Any of the preceding would be great examples of things that could allow you to move out of the apartment, provided you give the apartment notice and an opportunity to fix these things (and they don't).
If you're simply seeking to leave a residence that is in good, habitable condition, then you'll be risking legal action from the landlord.... even if the landlord does not have an original version of the lease.
This is AVVO, a place for users to obtain general legal information to general legal questions. I am glad to help you in any way I can, within those limits. I wish to make clear I am only communicating with you for the sole purpose of exchanging such general information, and nothing more. It is not legal advice, which I can not provide because among other reasons I know few of the necessary details of your situation. I do not purport to represent you in any way, shape or form. Of course, if you would like to seek out my services, and if you are a NY resident, I will probably not put up very much resistance but representation would still necessitate a signed retainer agreement between yourself and I. Thank you