Mexico - Meeting Place at MEX International Arrivals

I will be meeting a friend after arriving from LAX. Does anyone know of a meeting point after Immigration & Customs? I will be arriving earlier than my friend and will have to wait for an hour or so.
The same evening I will be on a BA Club class flight to LHR. How much time do I need to allocate for that?
Thank you.

You don't say what airline you are coming in on, since this will affect your terminal. AA? BA also leaves from T1 (if you have status with BA then the Mexicana lounge is slightly better than AA's).
T2 is mainly Aeromexico and its Skyteam partners (main exceptions being CO and LAN)
T1 is very long and spread-out. This thread on TA may be helpful to you:
http://www.tripadvisor.com/ShowTopic-g150800-i164-k3244113-l23076584-Where_should_I_meet_my_friend_in_Airport_Buses_to_ Cuautla-Mexico_City_Central_Mexico_and_Gulf_Coast.html#230 76584

I will be arriving on Alaska and leaving on BA. I will be meeting my friend landside.
Instead of waiting outside of Immigration for over an hour, is there a Lounge I can use? I am traveling First on Alaska and Business on BA.
Would the lounge have a phone from where I can call my friend's mobile and coordinate the time to meet?
Thank you very much.

I will be arriving on Alaska and leaving on BA. I will be meeting my friend landside.
Instead of waiting outside of Immigration for over an hour, is there a Lounge I can use? I am traveling First on Alaska and Business on BA.
Would the lounge have a phone from where I can call my friend's mobile and coordinate the time to meet?
Thank you very much.

The AA and MX lounges are airside, and they may want to see an onward boarding pass before letting you in. [In other words, if you are without your BA boarding pass, they may or may not let you in.]

Wireless internet is free in the two lounges [with Mexican's infinitum network user ID is mexicana@promocion and password panf24]. So if you can use skype or some other VOIP-like capability off your computer or wi-fi enabled phone/PDA, you could make calls that way. I don't recall seeing pay phones in the two lounges, but I wasn't looking for them either.

Landside -- after immigration and exiting customs -- at Terminal 1 are pay phone-type facilities, ranging from the coin and/or credit card operated to the manned bank of phone booths. Airside there is some kind of pay phone facility too.

Sometimes when I have to meet someone landside at Terminal 1, I designate the landside, relatively overpriced Burger King restaurant as the meeting point instead of the Camino Real hotel that is a walking path away from the terminal.