I've always thought that "high knees" was a poor verbal cue for what runners want to be doing. But to answer your question about the biomechanical cause of poor knee lift.
Weak quads, weak hip flexors, running with the pelvis tilted back (butt back) instead of tilted slightly forward.
What are the fixes? Well, does it really need to be fixed? I can't see her run so I don't know, but if it does need to be fixed here are some thoughts.
Reebok bench (8") heel drops progressing to heel drops while holding a dumbbell
Air squats, skater squats, jump squats (all done without weights)
fast 1 leg hops done in the Bulgarian squat position
Prime times
High knee drills
A skips
Lunges
Carioke
Low (8-16") box jumps
1 leg hops 10x each leg
Pogos (like jumping rope, but getting a little higher and/or hopping forward a little)
Very steep hill "sprints" of 15 sec. She should look ahead (not down) and focus on powering up with each step, NOT on getting up the hill as fast as possible. There is a tendency to hunch over and shuffle with tiny steps up very steep hills. Don't do that. This is a drill... the objective is not to get up the hill as fast as possible. The objective is to build leg power.