trips to south american in the summer (winter in Lima) are usually expensive as they are around the Christmas Holiday season. Kids are out of school, many people come to the US for vacation and many people originally from latin America go back home for vacations.
I doubt you will find anything cheaper LAX to LIM 2-3 months away and you are not flexible.
as far as internal flights, in Latin America (except maybe Brazil), these are expensive because of lack of competition and limited flights. In Argentina one roundtrip flight goes for $300+ unless you are a local resident. Foreigners usually pay higher fares.
If you are not flexible, buy the flights.