1. Yes, as I understood you should collect it later that day, though I forgot that detail, didn't tell the guy everything would be in the same day.

2. Yes there is locker service but I'm almost sure it is not pre-aduana. Here's the airport page and if you click on "ubicar" it looks like it is in the right said of the airport near the entrance, and it clearly mentions it is public zone, not passengers zone.

https://www.lima-airport.com/esp/par...on-de-equipaje