It seems to be a rather expensive route as a rule. It might be cheaper to fly from Lima to Juliaca and then take a bus to La Paz from Puno. LAN and Avianca have residency restrictions on the cheapest fares on this route, but perhaps Star Peru and Peruvian Airlines fly to JUL, they don't have any residency restrictions. On the other hand, LAN is now running an offer 20% off their flights in South America till 23 April, select the US as your country of residence on their website to take advantage of it.