KLM but you would have to connect in AMS. You can book the LAX-AMS-LAX segments either as NW8602/NW8601 or as KL602/KL601, but they are on KL metal. Generally it is better for U.S. residents to book them as NW-coded flights.
We are returning thru VIE ourselves on 9/23 on KL/NW (VIE-AMS-DTW-MSP).