I have a 2045 arrival into LIM from MIA on AV, and a departure to CUZ on LA at 1615 the next day (a Monday in June). I want to spend some time in Lima, and am considering the following two options:

1) Spend the night at an airport hotel, get up early, check into the CUZ flight, then head out into the city for a few hours, before heading back to the airport (and walk straight to the security line). I know that there's traffic into the city in the morning, but that should be manageable. I'm more keen to eat a good lunch, so want to leave the city as late as possible. Is this plan even workable, i.e. can I check in at 0800 for a flight at 1615? Different airports seem to have different policies on this. If it works, with boarding pass in hand, can I leave the city at 2pm, or even later?

2) Spend the night in the city, and check-in closer to departure time. I know they advise you to arrive 2 hours prior to departure, but when does check in close? When is the latest I can leave Miraflores if I want to catch the 1615 flight? I'm flying Y and don't have status on OW.

This is my first time in LIM, but I'm a regular at chaotic cities/airports across Asia like MNL, BOM, DEL, etc.

Thanks!