My first horse was so stiff to the right it was like riding a different horse when he took the right lead! This is the horse I trained to some pretty high dressage levels.
I will say that the lateral work does a lot. Eventually this horse would take either lead and do 1 tempe changes. He was ALWAYS different to the right.. (I got him when he was 7 and had been used a LOT). He was never real pretty to the right. He was balanced enough to do it when asked.. and he could actually collect and extend and stay on the right lead.
It did take a lot of work to get that with him.