Lounge access in SCL, as GRUflyer said, is available to:

Passengers DEPARTING SCL on a W or J seat.
Passengers with elite oneworld categories (Sapphire, Emerald)
Others, based on co-branding agreements.

Arrivals don't get lounge access

If you really need to, you can pay (although it's not cheap, around 55 dollars) to get access, but I don't think is worth the while.