Also, its appropriate to add that DL's JFK T4 concourse is insanely long. If your plane parks at a gate towards the end, it could take a while to walk towards the terminal exit.
TCONs from LAX typically park within a couple of gates of the SkyClub (and widebodies can't use the high B gates at the far end). When they don't the usually arrive in T2.
That said, it's still a solid 10 minute walk to the AirTrain, then another 10 minutes to change terminals (if the AirTrain is running normally), then clearing security. Theoretically doable, but I wouldn't try it.