The only thing I would add to this is that I flew on IB back in May, and they directed me to use a different lounge (not the AA one, or the Amex one). That was truly horrific, sort of bus waiting room like. After they had asked me for feedback on an ipad, and the manager had come to see exactly what was wrong in response to my feedback, I remembered that I was also able to use the AA lounge. Which was much, much better, even if it had not changed since I was last there, about 15 years previously.
So yes, the AA lounge in MEX may well be rubbish cf the rest of the World, but cf the other lounge offerings in MEX, the food is better, the furniture is better, the ambiance is more relaxing and it is quieter than the chaos anywhere else in MEX. MEX is an horrific airport, truly staggering the president came to power and canxd its replacement.