I wouldnt recommend lunging off the bit either, it is best to use a well fitting halter or a cavesson as Kristy has suggested.
When teaching a horse to lunge they need to learn simple voice commands which can also be applied to riding. Short commands like 'Move On' and 'Wooo' are the easiest to start off with. If you are having trouble with the horse going too fast put some trotting poles down and when she's going to fast just say in a calm voice 'Easy" and so on.
I found with mine that I don't even use a lunge whip, it tends to make them go to fast even when pointed away (these are TBs off the track). I just use the excess of the lunge line gently tossing it toward there rump to keep them going in the desired gait etc. All the best