I recently did HNL > LAX > JFK > LHR > CPH. My layover at JFK was 16 hours overnight. I did ask the AA agent if my bags could be checked straight through to final destination however was informed that bags could not be stored overnight at JFK on such a long layover (greater than 12 hours, I think). She said the system did not permit her to do it and therefore they would only be checked to JFK.

In any case there is a left luggage facility at Terminal 8 but it closes at 10PM.