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While you are technically in breach of contract, this particular term is unenforceable as it is illegal.
The vehicle owner must get their own title to the vehicle (and their own plates). The illegal portions of the contract must be disregarded and the remainder of the contract enforced.
You do not give the state you are in, but you simply need to go to the DMV for your state and complete a transfer of ownership for the vehicle. The buyer (the one assuming the lease) needs to sign. There will be a fee for this, the two of you can work out who pays for this fee.
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Yes, you still need to do the transfer with the DMV, if you do not do this, you are still going to have the liability issues you noted in your original question.
You will need to contact the NY DMV directly to get the proper forms for transferring the lease title mid-lease.
The information I found readily available was for either transfer of a vehicle that was owned, or for an initial lease vehicle (http://dmv.ny.gov/registration/register-leased-vehicle), but they can assist you (you will likely need to complete an affidavit).
It is a simple process, but you must do it - you do not want to be listed as the registered "owner" of the vehicle if you no longer have an ownership interest in it.