According to the NYS Department of Motor Vehicles notes that to replace your driver's license if it has been lost you can apply on line, by mail or at a local DMV office. There is a fee for obtaining this duplicate license.

If your driver’s license was lost or stolen because of a crime the DMV states that you will need to get form MV-78B from a police agency and fill it out. Make a copy of this form your records and then fill out the DMV form MV-44. Bring both these forms to the DMV office and show proof of identity. There is no fee to replace your driver’s license if the MV-78B form shows that your identification document (license) was stolen.

If you are afraid that someone will find your driver's license and commit identity fraud or identity theft with it then you may want to request from the New York DMV a change in your license number instead of just issuing you a duplicate of the lost driver's license. The DMV should be able to advise you if there are other steps you can take so that your license can be flagged for any unusual information request, etc.

The New York Consumer Protection Board should also be able to give you advice on how to protect yourself from being involved in identity theft even though you have lost your license.