Is he fine when you lead him to the right (like walking around the rail of the arena, tracking right ?
Do you ride him?
He's probably not as comfortable to the right so he rather not go that way. But obviously he needs to. I wouldn't put him on a lunge line just yet.. as he can get tangled up and hurt you or himself.
Free lunging is another option (what you have been doing) but put up BIGGER boundaries like if he switches direction, cut him off and send him the other way HARD. I would only get softer once he listens and is paying attention. Don't ask nicely first or you'll get ignored or worse, challenged dangerously.
Please be safe, though! Have someone with you when you are working with him despite whatever you decide to do as it is always your decision!
Good luck :)