I'm fairly certain the LIRR machines at Jamaica are AFTER you emerge from the Airtrain turnstiles. As you enter the LIRR station, there is a machine on the left, but it's been out of service for months. If you walk past all the tracks, there's a functioning one in the corner on the left past track 1. (You can also take the elevator there downstairs where IIRC there's another machine and of course ticket windows.)