There are many parking garages in the neighborhood. These two are the closest:
Lincoln Center Park and Lock Garage (Self-Service)
Lincoln Center's own garage is right on campus and allows you to reserve your spot in advance. Entrances are on 62nd Street between Columbus and Amsterdam (South and Westbound traffic) and 65th Street between Amsterdam and Broadway (North and Eastbound traffic).
To reserve, click here or visit https://parking.com/nyc/theaters/lincoln-center-theater.
North side of West 65th Street, between Amsterdam and Broadway. May also be entered from West 66th Street