LAX has 2 sets of runways that are basically parallel to each other. There are two south of the terminals and two north of the terminals. There is also a heliport but that’s not what you are talking about here, right?
The most common is landing to the west and taking off to the west.
Between midnight and 6:30 a.m. all departures are to the west (“Over Ocean Operation”), even if there is a tail wind. However, some aircraft do request departures to the east when other aircraft are departing to the west during the post-midnight hours. This usually happens when the tail component is too large for the weight of the aircraft.
See LAX Rules and Regulations and Noise Management