As I recall, Iberia's lounge (Premium Traveller) will stay open, AA will try and persuade you to leave about an hour before departure. The lounges are about the same, not too exciting frankly, but better than nothing. That said, the lounges are nearish security / check-in area, but the BA departure gate is quite a way from the lounge. MEX is a very long, straggling airport, BA's check-in is at one end - the far end on the oneway traffic system, the flight departs the other end, or so it seems. The other oddity at MEX is that check-in opens much sooner than normal, details in Manage My Booking / Check-in / Other ways to check in. I can't really see why, except for a few peak days MEX is no more or less efficient than any other airport to get through, so turning up 90 minutes before departure would give plenty of lounge time. I guess the traffic to the airport is somewhat variable to put it charitably, but there is a metro service.