cornellalum-- In that case, Im fairly confident that checking in your bags will not be a problem. Collect your bags after the LAN flight and head to the Aerolineas counters.

Considering you have some 2.5 to 3 hours, I would suggest you hop on a taxi and head to puerto madero, where you can have lunch and also walk around a bit. Ive recently heard good things about Chila, but there are plenty of other options. Just stay away from Cabaņa Las Lilas.