I don't know about cost but right now there are no direct flights to Lima from the DC area...
There are direct flights from Miami, New York JFK, Los Angeles, San Francisco (LAN), Miami (American), Fort Lauderdale (Spirit), Houston, Newark (Continental), Atlanta (Delta).
Probably the cheapest is Spirit but someone told me that they'd seen decent fares with Delta... If you want really cheap tickets you're going to have to look for a sale...