I am assuming that your friend gave you permission to ask for a constructive critique here, no? I will procede on that assumption.
First of all, the video is very nicely done. I see some nice editting and cinematography. However, as a video for critiqueing ground work techniques , I don't get much of each segment before it jumps to something else, so kind of hard to see what is really going on.
I don't see any real "work" happening there. I see a tolerant and kind horse going around with little interest in the doings, but being a very polite fellow, and a cute girl , kind of drifting around and being very sweet to the horse. Nothing bad happening, but no work happening either.
The first thing to change is don't ever lunge or do ground work with a chain on the lead. The chain is to go over the nose of an unruly horse who can be handled well by NO other method. Don't use it, period. ok?
SEcondly, don't lunge with loops in the line, held in the leading hand (hand closest to horse's mouth). Never hold a line with loops in it. you know why, I think. The excess line should be held in the off hand (the one not nearest the horse's mouth), and in a zigzag, not loop, manner. It can be held in the leading hand if you need, but NEVER in loops.
Now, when working with a horse lunging, you don't back up. YOu move the horse to where you want him to be, you never back yourself around. lots more to that, but let me leave it at that for now.
when she was leading the horse and she came to a stop, the horse kept going ahead of her and she lifted the line and he kind of drifted to a stop. That's something that needs correcting and that's where I'd start the actual "work" that we call ground work.