FWIW, I recently had a Spirit flight departing LIM around 11:50 p.m. where I checked in around 9:30 without much problem, but YMMV. They said to head to immigration sooner rather than later, so I did. I think it depends on the number of other flights, as they were set up for a much longer line than they actually had at the time, indicating that other times could have much more in backups. I think there's an exit tax or extra stuff their own people have to do (as there was a booth where a guy examined passports early on in the line), but something like that could slow things down even if it doesn't apply to you.