That's a perennial problem at our barn, I'm riding a new horse right now who has a lot of trouble picking up the right lead. He's getting tired of going around to the right in endless circles . . . but as soon as he gets it I canter down one side, hop off, loosen his girth, and walk him out for a drink. He's figuring out that GOOD things happen when he takes that lead . . . .
I actually do the opposite... I do think some horses who have been allowed to be one sided have difficulty being balance and coordinated on the off lead. But I think the only way to get them balanced and coordinated is to make them do it. Once they get in it, I keep them in it long enough for them to loosen up and find their rhythm. If you quit as soon as they do it, they don't get better. It's like writing with your off hand. If you quit after one word, you haven't taught your muscles anything. I do this on the lunge as well.