I too never lunge off the bit - I would never want to be in the position of pulling my horses sensitive mouths on purpose or accidentally. I always use a cavesson or a headcollar.
I don't use any auxiliary reins but have learnt how to help the horse to achieve balance and straightness through its biomechanics rather than artificial aids.
It really does help if you have someone who truly understands to teach/help you in the first place. You must be absolutely clear about what the purpose is and how you are going to achieve it in order to help your horse.
Hope you don't mind me asking, if you're using long lines successfully why do you want to lunge? Are you able to circle with the long lines? Oops just read you original post.
Perhaps her education is past lungeing? I believe you can do more with long reins/lines. As for lunge lessons - perhaps you could use another horse?
