Arriving at 8:00 should be more than adequate since you'll miss the traffic and the mob checking in for the late flights. TBIT has a decent food court landside and a few shops with fashion and LA souvenirs but it doesn't take long to end up standing around waiting for LAN to show up around 8:00 pm. Like carlosdca said security is usually pretty fast by around then since you'll be in between the waves heading across the Pacific. If LAN shows up at 8:00 you should be in the lounge by about 8:30. Hope you enjoy the trip!