They open at 4:30pm, 4.5 hours before departure. Generally in Mexico the recommendation is that you arrive for international flights 3 hours before. The desks are in Zone F3, upstairs in T1, at the north end of the building, next to security. Also bear in mind that you can't use mobile boarding passes at MEX, there are no self-service machines and I'm not sure if you can print your boarding pass either.

Haven't got any experience of the lounges unfortunately, but if it helps, the BA242 generally departs from gate 31. You're also probably better off getting something to eat before going through security - there's a bigger choice of food outlets upstairs in Terminal 1.