Where are you flying LAN to? Cuzco? We flew on Lan about two years ago or so. Lots of backpackers travel to cuzco not dressed to keen if you know what I mean. I would just have backups just in case. Don't know the dress codes, but we were dressed from our IAH-LIMA flight and just waited a few hours for our connection to Cuzco. So dress code was without question if anything, OVERDRESSED. I wouldn't take a chance about not making a connection because of a shoe situation or pants for that matter, or collar shirt. I know you are probably the type that likes to dress casual, but is wearing a pair of shoes, slacks and collar shirt that much like pulling teath? Good luck in Peru. You will love Machu Pichu.