I used to have your EXACT same problem! I don't know how I fixed it, it just came natural. My coach reminded me that I had to GET UNDER the foot because I would ALWAYS grab the side of her foot with my left hand and have four of my fingers on top of her toes, while the thumb was the only thing up underneath her foot.
Try pushing her straight up and not to the side. Think center when you're pushing her up for the lib and push your left hand over more to get directly under the foot. Really, even when you get the grip right, the weight is still going to kind of be on the right hand; the left hand is really just to stabilize her and give her something to stand on, as told by my coach.
noodleashy is right about the grip, that's the best way you can explain it. Good luck!