HOwever, Lizzy looks like she might accept more rein contact, if it were offered in a steady manner, and she might round a bit, and then step under more, too.
To do that, work at the walk. You post pretty well and your balance over your leg has improved a ton, so you have become a lot more independent there. But your elbow is still a bit straight, locked, and with a downward angle to the arm . It looks a bit like you are trying to pull her down, but in any case, the all important straight line from elbow, thorough wrist, to bit , is not there.
Sit down, start at the walk and "find" her mouth. This can be done like this:
Start with loose reins, just feeling her walk with your body and getting your seat and your following hips, which I know you can do very well. Then take your rein up a bit and move your hands out like you are forming a triangle to the bit , or , say, pushing a wheel barrow. When you make contact with the mouth, work on following it so that the rein never gets either tighter or looser. You'll have to move forward and backward. It's your shoulder that will be moving, but it helps to think of it more as your lower body goes forward, toward the "triangle" you have created, then back, then forward, then back. But the actual movement will occur in your shoulder and elbow. Whatever, just really feel the mouth and keep that steady contact. Your elbow can come away from your side, but do not have your hand pointing further down than at a direct line to the bit. Think of your thumbs as laser guns that must point directly AT the bit.
When you are really following the horse's mouth, then you can walk your hands up the reins a bit (inch them up) to shorten the reins, and bring your elbows back in to your sides (the "triangle" becomes narrower). Do this all within the walking rythm of the horse. Don't loose the horse's mouth . And you can then be a bit firmer in your outside hand, and a tiny bit of a "tickle" on the inside rein, and the horse should flex to the inside and soften to your hand a bit. Now, ask for a bigger walk, get a few really active steps, stay with your big walking horse, then reward! Release the inside rein really big, like looping down, and praise your horse!
Rinse and repeat.