There are no airline specific lounges in the Lima airport. However, there are 2 lounges in the LIM airport, and both of them are on the international side. I have only been to the VIP lounge and you might be able to get into it with a little bit of persuasion and your business class ticket. However, without status, they may not let you.
Correction: there are 3 lounges in the Lima airport. Still don't know what the requisites are per each, though.
There are three VIP lounges operated by airlines and other organisations, the Peru VIP Lounge; the VIP Club Lounge for first-class passengers of specific airlines, and the Authorities Lounge. Diners cardholders may use the VIP lounges in the terminal.
The VIP Lounge in LIM is air-side and there's only one terminal for all international flights. In fact, the entire airport is essentially one big terminal... the domestic and international sections are divided, however.
If need be, the Starbucks outside of security is open 24 hours, so there's always that option.
A couple more tips, tricks, and hints:
- Don't ever leave your stuff unattended even for a split second, crime is rampant in the Lima airport (yes, inside the airport terminal)
- While going through the check in hall to go back through security, do not make eye contact with anyone and constantly say, "No gracias". They are trying to offer you rides and to carry your bags and the like. Again, crime is bad.
- For a wider range in food selections, eat in the food court outside of security. On the international side there is only one (maybe two?) restaurants and the rest is just trinket stores. And I do not believe that there is a way to come back out of the security check point once you're through.
- There is free wireless internet throughout the airport and you should be able to find power plugs. If I remember correctly, they do use the US plug formats, but double check on that.
- Have fun at immigrations and enjoy the red light/green light
- Make sure to order a Pisco Sour... yum!
If I think of anything else, I'll come repost.
Hope that helps.