I cut engine one to see what would happen. You can still fly the L1011, but it's not easy, and you have to compensate for the yaw and hold altitude and speed... I'm not sure I would trust the autopilot do do this or want to finish a flight. (Not sure I'd want to land, either!) The better news is it's easy to relight the engine. I just switched it back on, and used the conveniently located "windmill air start" button on the overhead right below the ground start buttons. I was actually kind of impressed at the results. The passengers, not so much. Fun times for an airplane that isn't a "study level sim" (as I keep being told) where failures are a feature.

Much less fun if you have a 3 engine flame out! If that happens, you have to hope you are at a high enough altitude to get them all restarted using windmilling, or you're doomed!
You could try doing a restart using the APU if you have enough altitude.
I'm pretty sure I managed to start them after this happened at cruise altitude (~FL320), and I'm pretty sure I manage to restart them using the APU.

So, you're not going to share how THAT happened?  :)

It was so long  ago, I'm not sure how it happened. If I remember correctly, I did it deliberately to see if I could get the engines restarted (think Speedbird 9 - 24 June 1982 (although that was a 747-200, not an L-1011)). I just wanted to see if it could be done.

I tried an all engine flameout at 10,000', but that didn't end well. :(