I'll give the complete steps (checked luggage included) just in case.

You'll go through immigration first, then it's baggage claim and customs (if you don't need to declare it's usually just leaving (no form needed unless you are declaring something) and usually no further checks. When exiting you go straight ahead to the departures area check-in (LATAM is closest on this end), you should've been able to check-in online, you can print the luggage tags here and drop off. From here, I would suggest backtracking a bit to the escalator to the second floor (this is usually better than going all through the rest of the check-in area), then turn right and go straight ahead. There is first left if you want to go to the departures security or keep going straight ahead if you want to pass by the shops/café/Starbucks/food court beforehand (you can go through all of this, keep turning left and end also at departures security). If I recall correctly, there are enough signs, I might be biased as it's my home airport but I think it should be pretty easy to get around.

There are also maps here: https://www.lima-airport.com/en/mapas

After security for domestic flights (you can take liquids through) there are a few shops, a lounge and another Starbucks. A few departures are from the lower level by bus, some are on the same second floor (regular jetways).

Have a nice trip!