Two things that I've found to help the younger kids when a lamb is dragging them around. First, teach them the "emergency break." Most kids will tend to wrap their arms about the throat of the lamb and what happens then is that the lamb will lower its head and run away with the kid. Instead, have the child hold the lamb under the jaw with the left hand, closer to the lamb's chin. When the lamb starts going to fast, they can crank the lamb's head up and back, (emergency break), taking the leverage and power away from the lamb. Even a small child can control a fairly large lamb using this method.
The second thing we do is keep a halter and the lamb and have an adult hold the end of the halter lead. If the lamb gets to overpowering the kid, the adult and pull back on the rope. Obviously this won't work in the show ring, but it can help to break a bad habit and trick the lamb into thinking that it cannot overpower a smaller kid. It also helps to control the lamb until the kid can gain some more confidence to control the lamb himself. After all, that's really what it all is. If a kid believe he can control a lamb, he can. If he believes he cannot, the lamb will drag him all over the place.