I don't lunge with boots.... I don't ride with boots either unless I am jumping and when I am riding I do circles, my horse is fine.
What I lunge in is a cavesson and that's it, but before I got it I lunged in halter.
If I were to get side reins I would lunge with my saddle and attach the reins to the girth, you would need them on the losest one at first for your horse to get used to the contact, then gradually tighten it.
You should never force your horses head down though.
When lungeing I practice tranisitions mainly walk trot walk and only really do canter once on both sides, for a whole circle, as Buzz is still slightly unbalanced at the canter.
If your horse is an OTTB he will be extremely unbalanced unless someone else has already put time into him, but you may be best just doing walk trot transitions.
Also make sure you have the lunge rope as big as possible, smaller circles are harder.
Well boat load of info.... hopefully some of it made sense lol