Get a copy of the license from the NJ DMV or whatever they call themselves. Then go to the NY DMV where you will only need to take a written test. The manual is available on line, so give it a quick read through.Without the Jersey docs you would probably need to take a road test in NY.
By lost I take it you mean taken by the cops. You re going to have to take the written test AND the driving test all over again. Get an appointment with the DMV for the written test, pass that, then schedule your driving test and pass that. You ll also have to have proof that you live in NY now.