That may be the case here. She is doing exactly that, and it is an immediate response. At first, I thought maybe she had actually been hit with the whip in the past, and was turning her hind quarters away from it. I don't think that is the case, however, because she shows no fear of the whip at all.
Most horses have that response to a whip on the hind quarters if they've never been taught anything else. It's just natural. You're trying to whip something and they're trying to hide it so you can't.
Try breaking the act of asking her to go forward into steps. First, lift your arm holding the lead up to shoulder level, pointing in the direction you want her to go. Pause a second, then cluck to her or what ever signal you want to use to say "go forward", pause a second, then lift your whip hand, pause, then swing the whip hand like you're going to tag her with it, but don't, then if she still hasn't responded, tag her with it, hard, but on the shoulder area. This should startle her enough to take a step or two in the direction you want her to go and that's all you want for now.. Just repeat until she starts recognizing the steps that happen before she gets tagged and will react quicker to avoid it. Finally all you'll have to do is raise your lead arm and she'll move off. You can worry about the circling and more advanced stuff later.
I know you're getting lots of conflicting advice. We all do things differently. Just do what ever works for you.
She certainly has been hit with it, I would assume, and FWIW, so has Lightning, and any other horse who moves away from it. Horses don't learn to lunge having never had the whip or the end of the line, or whatever you are using, touch them. They don't learn to respect it because of anything inate about whips, if they didn't know it can reach them and it hurts, they wouldn't learn to move when it moves. Most horses don't fear the whip as an inatimate object, they fear it only when you apply it... It's your body language with it that they might fear, not the object sitting on the ground. Some who have been overly whipped fear it too much and it can be a distraction. It's a balance. Actually hitting them with it is fairly rare with a fairly responsive horse. It shouldn't be used on a confused horse who doesn't know what to do, but rather used to enforce a command when the horse is lazily ignoring a ~known~ command to trot or canter from the walk, for example.