Your problem is that LP has no brasilian partner, so wherever you go from Brazil, you will have to fly via an LP airline hub. Also, AFAIK, only Avianca fly out of Rio (to BOG). Others fly out of GRU: Copa to Panama and Taca to Lima. That is it, I am afraid. The only other LP airline (Aeropostal) only fly to Northern Brazil (Manaus and Boa Vista)