Letting him lose condition like that = incredibly bad thing.
But...something I think needs to be said is that NOT every horse can make a good lesson horse. Some of them seem to be born to it, and some will never get there. That's how I got my horse. My trainer bought him for the lesson program, and he didn't do well. He was willing, but sensitive, and he just got confused as heck by having a bunch of different riders. It stressed him our. She realized within a season that he was basically a One Rider Horse, so she sold him.
I have someone else ride him from time to time, because I need to go away and he needs to be exercised, mostly...but the other person is a better rider than I am too, and can do things with him that I can't yet. It's good for him, and he seems to be able to keep 2 riders straight in his head a lot better than when it was "chance draw of the day" in the lesson program.
Could be that your Barney isn't cut out mentally for the lesson-barn life. That would be something his owner might want to keep in mind, although, once she sells him, she doesn't have any more control.