LIM is not upgradeable on a Q fare. Southamerica means all of Southamerica (not just deep SouthAmerica).

As Hayden points out, the difference between Q and the next fare bucket can be quite small. If you have not ticketed, call AA and ask them how much the difference is. It would probably be well worth it LAX-LIM. But before pulling the trigger you might want to ask the availability of the upgrade using miles.