Well I took four LATAM flights recently LAX-LIM, LIM-CUZ, CUZ-LIM, LIM-LAX and not one of them was on time. In order of taking place: 3.5 hours late, 2 hours late, 15 min late, 30 min late. Pathetic, esp. the two long delays!!

You could try to get on LAN 601 LAX-LIM which arrives at midnight, you'll have to crash in the airport till you can get on the next EZE flight. The seats in the terminal do not have armrests so laying down is doable.