Mexicana 3-hour rule is informed to all pax as several will travel with lots of luggage and their kitchen sink, thus it takes a long while to sort it all out and issue boarding passes.
Check-in 1,5h before and you should be fine to get your boarding passes, clear security and visit anyone of the OW lounges available at that terminal. MX should inform which lounge they use at JFK as well, to invite you over.
At Cancun, because of your being BA Gold, you are welcome to any MX Business (Clase Ejecutiva) queues and lounge as they are a One World member.