Lift you hand or your rein? Or both I guess? I'm not an expert and I ride English, but I have always had a problem with my gelding dropping or leaning out on a shoulder. Don't lift the rein, that just lets the shoulder pop underneath it. I would lift my inside rein to keep my horse from dropping his shoulder and my trainer said to me, "He's 1100 pounds, there is no way you are going to pick him up with that little rein." It was a tough habit to break.
When he leans to the inside or drops that shoulder down, pull the rein down and back to your hip instead and apply your leg. Then take him a little on the outside rein to straighten him out.
Give that a whirl.