Hi Beckoa,
I am actually connecting in Mexico City in April and I went onto AeroMexico's website and chatted with a nice person. The representative told me that per the Terms and Conditions they do not Interline with TAM and I'm assuming the same is for LAN as well. TAM and LAN are located in different terminals and you have to clear customs in Mexico City and forward your bags to your next carrier.
Sounds like a pain to me but oh well I'm not complaining because I have 12 hours to make the connection and hopefully have time to tour Mexico City. The ticket was $474 per person one way to catch a cruise to Barcelona.
Hope this helps but I would confirm this with AeroMexico.