Ooops...I misread that part. Umpire might have been clueless, too!
Breaking it down...
"Runner on third, leads off is about 1/3 of the way home on the pitch"
Everything's cool so far...
"Catcher has ball walks towards runner runner stays put"
Still cool...
"Catcher lobs ball to pitcher"
Now we're finally getting to the meat of the question! There is nothing up to this point to restrict the runner's movement or force her to go one way or the other
The Look Back Rule goes into effect the instant the pitcher has the ball in the circle (and is not making a play). If the runner is off the bag and in motion at that instant, she still is allowed to stop one time, then immediately either advance to the next base or go back to the last one. She could keep moving forward to within one inch of the plate, then stop and head directly back to third. Or, just keep on heading to home. Her choice and all perfectly legal.
If the coach complained about the runner's move, his complaint was groundless. If the umpire said she would have been out if she had headed back to third, that isn't right either.