I would suggest she hire a dogwalker, and talk to a service dog trainer- perhaps the dog can be trained to pre-alert her to seizures and thus make her more mobile? many persons with seizures use such dogs.
I could probably get one of my trained agility dogs to “lunge” without any additional training because they are taught to follow my indicated direction/speed/distance. I wouldn’t bother with a whip with a dog; dogs are Chasers rather than Chasees, so being chased by a whip wouldn’t really motivate them. Perhaps put a cone out, and teach the dog to go out and move around the cone, and then put two cones, and move around the two cones, and build up to a small circle of cones, gradually making the circle bigger?
I think that would drive the dog crazy with boredom, running around the circle endlessly once the trick was mastered, but teaching it might be fun for the dog, and certainly will be fun for the owner.
I don’t like to see people try to jump dogs while they are on lines, so until the dog is trained sufficiently to focus and obey while off a line, I’d bag that one.
Teaching the dog silly tricks is always a fun way to work their minds. Some “tricks” can be very useful- find the keys, fetch the remote, etc.
Other fun ways to work dogs at home: weight-pulling, flirt poles, rally training, agility training in general.
The dog clearly needs more work on basic obedience if he can’t be let off a line, so maybe she should start there.