Continental Newark-Lima $408 with taxes
Continental has some nice airfares on direct flights out of Newark to Lima. You might find these fares in December on Saturdays only, but I think the days expand in January, so lots of availability then.
AA has matched NYC-LIM $338+ tax ($400ish all in)
Not a direct flight, but connecting.
Major Deal on LAN From NYC March 3 until April 2
I know this doesn't apply to most people. However if you stay long term in lima and are from the NYC area check these dates out. I managed to get a non stop flight both ways for $495 which includes taxes. Restrictions apply ($100 penalty for changes) but I think it is worth the gamble.
LAN offers the most *comfortable non stop flights from NYC.
This is a great time to be in lima. The weather is good and people are in a good mood and excited about easter approaching.
One could get away with staying at a cheapo hostel during these dates. The only thing you might need would be a fan in your room.