International connection in Lima, Peru.

Can anyone give me an idea on how easy or hard is to connect through Lima between two international flights. I will be arriving to Lima at 11:00pm from the US and I want to connect with Lan to
Easter Islands at 1:20am. Is two hours enough time? Lan also has a flight from LAX/LIM/IPC but the connection in Lima is only 1 hour. Any suggestions? Also we usually travel with just carry-on but some airlines, due to carry-on weight restriction, check our rollers. What happens if we have to pick up our bags, do we have to clear immigration and customs then instead of just going through the transit area?
Thank you in advance, any information is greatly appreciated :)

I don't know for Easter Island but you should clear customs well under one hour, and the LAN gate was at the end of the terminal, just ask. No rides to anywhere that I know of. Just walk towards the other end of the arrival area as you clear customs, go to almost the escalators that leads to a restaurant, but the LAN terminal should be right there by the escalators, last booth in fact. (Should read "STANDBY LINE") If you miss it for that day, don't freak, just make Lima a go at it or go to Cuzco. Sounds like a win win to me. Have fun and hope you do make it to Easter Island. Great pick.