My personal opinion, don't get a rope halter. If a horse does something wrong, getting a stronger tool is not the answer. My opinion, which may be a longer more difficult way of doing it, but will get you a more solid horse in the end - is to teach the horse to lunge correctly.
Take him back to the beginning of lunging. Start with a long lead rope and a flat halter, use the lunge whip, line yourself up appropriately, ask for a walk, slowly let the circle get larger, if he begins pulling, make the circle smaller again - you went too fast. If he only pulls at the trot practice at the trot (you'll want a lunge line, not a long lead rope for that though). Start in small, easily controlled circles, ask for a nice trot, if he pulls ask for tighter circles. It sounds to me like this horse needs to be restarted in lunging.
Also - for what purpose are you lunging the horse? Lunging to me is an in between skill - not for everyday use. It's good for teaching your horse how to be sent away, it's good to teach your horse to drive forward from his hind end, it's good to practice gait transitions on the ground, but only walk-trot-walk-halt sort of transitions, cantering on a lunge is SO bad for their joints and unless your teaching students who are just learning the feel for a canter - I see no purpose in cantering on a lunge.
If you're looking to exercise him and keep him mentally active, lunging really isn't a good choice - it's so mind-numbing for a horse to just move off in circles. Get an extra lunge line and line-drive him, you don't need a surcingle you can use a saddle or even just a polo wrap wrapped around his girth area with some rings run through the polo to run the lines through. Personally I don't use either, I just let the lines hit their sides (it helps to build walls) you just need to be very careful not to let the lines get low enough for them to get caught in. Ground drive him all around his field, over poles, over tarps, through any obstacle you can make. This will help better him in So many ways, far more effective than just running circles.
Good luck with your horse :)