There are so many factors, but I don't see the leg lift as a primary problem. I see the problem related to mechancis, balance, rythym/tempo, lack of long-toss, hand separation, and staying closed.
Get your son a qualified pitching instructor. Tempo could be the problem. Strive to equally time the three parts of pitching: 1- Start to balance point should equal 2- Balance point to foot plant should equal 3- Foot plant to release.
Balance could be the problem. A lot of pitchers "bend their back" prior to the balance point (lack of balance). This lack of balance means this: The body will now focus it's energy on achieving balance rather than directing it's force downward to the footplant stage. To illustrate this, try lifting your leg to the balance point. Now bend your back until you almost tip backwards. Will your next action be to achieve balance or drive towards the plate?
Long-toss is paramount. For starters, it is hard to throw a ball far if you don't have good mechanics. Because of this, long-toss reinforces proper throwing technique and arm slot. Long-toss also promotes arm health by stretching the muscles and tendons. Finally, it promotes the most critical element of a fastball: Arm speed.
Hand separation should occur precisely at balance point. This has to do with rythym or tempo but also because 1) early separation impies "flying open" and 2) late separation implies rushing (arm cannot catch up and the ball will sail high or wide).
Staying closed. Get behind the pitcher. When the landing foot plants the ball, the pitcher's body and the landing foot and glove should be in perfect alignment.
Do a Google search and read about Alan Jaeger's long-toss method. Throw and long-toss year-round. Never stop throwing.