| Cheap Flights: Austin to/from Lihue-Kauai, Hawaii $371-$377 r/t [March-May] (limited availability) â Alaska Airlines Alaska Airlines has round-trip flights from Austin (AUS) to Kauai (LIH) for $371-$377 with a connection. Flights March to May. Departures on Tuesday and Wednesday. Origin/Destination reversible. Click for more details and booking links Cheap Flights: Austin to/from Lihue-Kauai, Hawaii $371-$377 r/t [March-May] (limited availability) â Alaska Airlines . | 