Both of my visits to Peru, I flew LAN round trip. Purchased through Orbitz- I'm not necessarily a fan of Orbitz, but they do pretty well for airfare. I have a lot of consolidator links saved, but Orbitz provides one of the most comprehensive search tools I have ever seen.
I know the option I'm about to describe says: US/Canada 0nly. Ignore that. Because they're lying.
Instead of selecting specific dates, there is a small link below the area for entering your dates called 'flexible dates.' Clicking that option provides three different options for searching: 1. Weekend trips(pretty obvious) 2. Bonus days, you can search for up to three days before and after the begin/end of your dates. and 3. Flexible dates. I like this one, it allows me to search up to 30 days for the best time to leave/return from my trip. You choose the length of your stay, the span of days(up to 30) to search, and it provides the results.
Even if you don't use Orbitz to purchase, its an excellent reference tool for finding the best price within a range of dates. I wouldn't recommend using Orbitz for hotels, but for airfare, they provide a lot of good information. One caveat: there are numerous airlines that I believe are not used by Orbitz, however I do believe they do have all the major airlines, domestic and international.
My trips(all booked through Orbitz) include: Dec $850, Feb: $650 and June(yes!): $578.
All three flights use LAN to Lima, and 0nly my latest routes me with a layover on my return flight(in Miami). You may or may not prefer LAN, they fly my route, LAX-LIM, 0nly once a day; late morning/afternoon to LIM, and midnight to LAX. Well, for non-stop service, that is.
If I were willing to fly with TACA, I could get to Lima and back for less than $500. There's a layover in El Salvador, but its still less than $500, taxes and fees included. That's pretty tough to beat out of LAX.
The best thing to do is start planning 4-6 weeks out. That way, even if you miss a low fare once, its almost certain to re-appear later on.
Hope I've been of some assistance here.
The Cap'n