This may sound a bit backwards, but have you tried lunging her without the whip?
I tried several times to get my horse to free lunge with a whip, and he simply would not. He would stand there and look at me like I was insane, or dumb, (probably both) and toss his head up and down.
The other day I just used a coiled lead rope instead of a whip and sort of swung that (still coiled) around to get my point across, and he went perfectly. I never had to touch him with it. All I had to do was, for example if I wanted him going to the left, I would point my left hand in that direction (about parallel with my shoulder) and raise the leadrope hand and off he'd go.
I walk a small circle in the middle (same direction as the horse) once he's going just so I can drive him better; just be sure to stay slightly behind the horse, so you're driving him forward from his hindquarters.
Also, never look at their face; I like to look at Beau's hindquarters when lunging but I also know of a trainer who looks at the shoulder when driving forward.
Fly Without Wings