LAN should check your bags through (although it may be on a handwritten baggage tag). You can also OLCI 48 hours in advance for LAN flights, and LIM/MEX is a route you ca *probably* obtain a boarding pass in advance. (Flights to/from the USA you cannot, I don't know if there are other routes.)

LAN has a customer ?service? counter (it is a counter ) just past transit security before heading back upstairs to departures.