My horse can be an idiot on the lunge line. Your's doesn't know how, but mine does. I'll put him on the line at a show, and ill just hook it to his halter instead of putting the chain on just because he doesn't normally like the chain. Normally he is perfectly fine and just does his thing. Well, the other day the lunge arena was wet, so I put him on the line out in one of the arenas. I hooked it to his halter like normal, and picked up the whip. He reared up, looked at me, and then stood there. I tried again, and got the same result. So, I walked over to him, put the chain on, and tried again, and it finally worked. I guess it goes to show that I can't always be so nice to him all the time.
Sorry, that really has nothing to do with your problem, but I just felt like sharing my little anecdote (:
Good luck with the mare, there are a lot of threads on here on lunging which I'm sure will help you!