wont lunge right.
All that you have said has me convinced there is some sort of physical issue. I would NOT try to force him to go right until you have explored this. The more you keep pushing this issue unsuccessfully, the worse your feeling for him and his for being with you will become. Stop now and try a different tactic, lunging is not necesary and I think might be harmful now.
Have you considered blindness in one eye?
If he doesn't want to canter to the right (or even go that way, but especially in canter) that says to me that there is some soreness or spine/hip misallignment or other pain producing issue on his left side. When a horse canters to the right, the left side does more of the pushing and load bearing, so if it's sore the horse will avoid cantering right.
Bucking when taking up the canter is a very common sign of some sort of hip or spine misalignment.
Does this horse roll when at liberty?
Does it back up well on the lead line, with reasonable freedom or does it drag its feet, and which ones.?
I guess if you can't afford to have it checked by an equine chiropractor, then I would do other sorts of work with it, maybe have it go over small cavaletti, and you can do this in a straight line. Back it up, turn it rt. lft. and do some carrot stretches. Work at the walk . Ride it up hills if you have them.
Dont worry about giving up on a lesson and walking away from it. Forcing the horse to go right when it is plainly saying "I can't!" will not make your dominance stronger, only build fear and resentment into that horse.
I know you want to make him a better animal and you have limits to work within. I feel your frustration and wish I had more positive help rather than negative. Bless you for your kind intentions.