All LAWA operated buses pick up at the inner curb and use the bus-only lanes. That includes the FlyAway bus, Airline Connections, LA City Bus Center, Lot E bus, and bus to the green line. The pickup locations for everything are listed in the
Wiki at the top of the LAXit thread. The lot E bus also goes to the off-airport rental car center as its first stop before Lot E.
Outer curb (islands) lower level is personal vehicles, TCP vehicles (including Uber Black and Lyft Lux), and rental car shuttles, and various limo services.