I always thought it would be cool if you had to hit X and change the grip on the lance to stab to the left side.
So over lance grip for right and couching and under lance for left. But! If your in under lance for the left side strike it should be like 130 degree range, perhaps even have more power but somehow limit it's speed bonus because it would be pretty hard to control at speed but it would work well for riding up and stabing at people on foot..