Don't know if it caught fire, but I was in a SW flight out of Dallas about 45 years ago, that shut an engine down about 20 seconds after takeoff.
Lights flickered, plane dipped, roar of two engines replaced by one at idle. Woke us all up a bit, especially the group in front of me who had never flown before.
I wasn't too worried, figured we had one good engine. Then the stewardesses (45 years ago, remember) started running around picking up purses and loose luggage, and making us do the brace.
After landing, saw the flight crew looking into the left engine as if they could find the problem
Landing uneventful, and they ran us on another plane to finish the flight to Hobby. Called mom and dad when I finally got back to College Station. Dad said ""It was the left one, wasn't it?
Yeah, I saw something dripping out of that engine before you left Lubbock."
(Back when you could still go to the gate to drop off)