Can't upgrade from economy to First on a three class plane offering three class international service, and no 3 class planes are sold as two classes except for the domestic trips like ORD-LAX, ORD-SFO, LAX-EWR, JFK-MIA and several others. Plus, those flights might be operated with a 762, which wouldn't get you a flat first class seat.
If you want International First in a sleeper seat, then you have to upgrade from purchased business class or pay for First.
My recommendation? Schedule ORD-LAX and upgrade it with stickers. Odds are that a star might be up front with you (I've shared First with plenty of celebs on that route, though not as many as JFK-LAX). After dinner you can stretch out that sleeper seat and nap the rest of the way to LA.
Have fun.
