I just did this a few weeks ago - flew MexicanaClick and transfered to LAN. Not sure what time your LAN flight is, but the LAN check-in desk did not open until 8pm. Keep that in mind as you will not be able to check bags (if not transfered automatically), or if you want to access restaurants/lounges on the secure airside.

The map on OneWorld was not a lot of help, if I recall correctly, as it indicates the train is on one end of T1 and it actually is in the middle. The walkway to the train is marked occasionally, and is on the second level (up escalators). Assuming that you don't have your LAN boarding pass printed by MX, be sure to have a copy of the itinerary, as it is checked before you can get on the train.