I think UA's earliest ex-LIM flight is the EWR one at 11pm, so you wouldn't be able to even check in before the counter opens for that flight, typically ~3 hours prior. If you're just connecting from domestic with a long layover, the bad thing about LIM is there's absolutely nowhere (safe) nearby to kill time, you'd need to go all the way to Miraflores or that direct vicinity, which can be an hour each way. There is a Wyndham on the airport property, but don't know if they have a good restaurant / bar to kill time in or not.