The process will be the same as if you hadn't paid any sales tax at all. You'll have to provide DMV with your lease agreement and fill out a Statement of Transaction at NY State Department of Tax and Finance. The sales tax for any existing lease payments you have will be paid to DMV.
Can this be done online?
No, you will need to do this in person at a DMV office.
I leased the vehicle in New Jersey and think I paid some sales tax there. Do I have to pay it again in NY?