LAN has kind of two checkin deadlines. If you haven't checked in three hours before departure, legally they might be able to deny boarding without having to compensate if flight is oversold... (http://www.lan.com/es_pe/sitio_perso...as-frecuentes/). On the other hand checkin desks tend to close about 60 (?) minutes before departure.

I wouldn't arrive less than 90 minutes before departure because of immigration and security lines...