As JL operates to/from terminal 1 at JFK you won't have access to an American lounge, but with Priority Pass you can also choose the Korean Air lounge. In my opinion, the Air France lounge is better and has a nicer ambiance but if you have an extended stay you'll at least have a couple of options available.

Food in the Korean lounge is not very impressive, even American does it better. And that's saying something! ^