The insurance company doesn t give a squat about the license plates on her car, or yours. You shouldn t have any problems adding her car onto your policy. Call your insurance company and simply tell them that you want to add another vehicle and driver. Of course, they ll want to know who the leasor is (bank or loan company) so they can apply the appropriate coverage for a leased vehicle, and also where the vehicle is garaged (NY).
As your question states we live in new york therefore both of you should have new york license plates. In most states you have 10 days after moving to get the proper license plates. Otherwise you are breaking the law and should be prosecuted for fraud.
not a travel question. ask the leasing company. i bet you cannot.