| First Class Nonstop Flights: Austin to/from Los Angeles $237 r/t [March-May] â Alaska Airlines Alaska Airlines has FIRST CLASS, NONSTOP, round-trip flights from Austin (AUS) to Los Angeles (LAX) for $237. Flights March to May. Weekends available. Origin/Destination reversible. Click for more details and booking links First Class Nonstop Flights: Austin to/from Los Angeles $237 r/t [March-May] â Alaska Airlines . | 