Do you have any status on AA or OW?
- If you have PLT (OW sapphire) status then you will have access to the AA FL (or AC), BA galleries and CX lounges at LHR (I believe JAL is closed/closing).
- If you have EXP (OW emerald) status then you will have access to the AA FL (or AC), BA First lounge and CX F lounges at LHR
- if you have GLD (OW ruby) or no status then you will ONLY have access to the AA FL or AC – I believe the FL is undergoing renovations so you will have access to the AC.

At JFK you will have access to the AA FL (within the AC on the closer side of terminal 8 at JFK)

In all of the above would add that if you have a choice (and status), definitely go for the BA lounges !