You can add MBJ to the list of Caribbean destinations with Business Class lounges. This one is an AA-only lounge, and an AC membership or status alone won't get you in.
The MBJ one is run by AA; the agents actually brought all of the J cabin folks from the lounge to the gate (it's a decent walk) and escorted us past the line of folks waiting to board (Y had started boarding) and onto the plane.
Free Red Stripe too IIRC.