I think lunging a horse in a flat halter will encourage the horse to lean on the halter. Leaning on the halter goes with leaking out through the outside shoulder, or it could be leaning on the inside, depends on speed and the hrose. But, it will have the horse leaning, most likely. Lounging a horse for excersize wherein it goes around leaning and in a very bad form will only build in a bad way of going, rigidity and soreness.
I would either lunge with the bit set up she has, with a surcingle and side reins. Or, use a rope halter, lunge on a smaller circle and work on having the horse keep a bend in it's body, it's shoulder up and not to lean on the leadline. Slower speeds would be most likely the way you'd do that. Then, once the horse is moving correctly, let it go in the arena and let it free lunge itself for excersize, and to get it's ya-yas out.
And to Cherie:
You do not use the whip? I mean, if you are going to teach the horse to go off from the whip, and it doesn't go after two asks, you said you make it sorry it didnt', but that does not include any hitting with the whip? Do you just whack the ground and make a lot of impressive noise and movement?