I want to double check lounge access for a few upcoming flights I have in Y and P. I have platinum pro status with AA. My understanding is that I have admirals club access for the international segments (ie MIA—PTY, JFK—>LHR) but I’m confused as to whether I have access for the proceeding segments like LAX—>MIA when my final destination is PTY or JFK—>LAX if I’m coming from MAD. If I do get access at LAX on departure would that extend to the Qantas and Business lounge? I’m confused as to whether the destinations of PTY and LIR would qualify for access?

LAX—> MIA—> PTY
LAX—> LIR
LAX—>JFK—>LHR
MAD—>JFK—>LAX