| First Class Nonstop Flights: Austin to/from Los Angeles $258 r/t [September-November] â Alaska Airlines Alaska Airlines has First Class round-trip flights from Austin (AUS) to Los Angeles (LAX) for $258, NONSTOP. Flights September to November. Departures on Tuesday, Wednesday, and Saturday. Extended weekends available. Origin/Destination reversible. Click for more details and booking links First Class Nonstop Flights: Austin to/from Los Angeles $258 r/t [September-November] â Alaska Airlines . | 