Well, EE, there are two ways to think about your question. Is the lead we are talking about the "apparent" one of the actual one?
Of the two, the actual one is easier to get a real answer to. To refine our thinking, we won't shoot a shotgun, but rather a .22 and the target is not a clay one, it's a nickel (which flies like a clay target, for the purposes here.)
So the question is how far must the .22 be pointed ahead of the flying nickel to hit it? And behind that are two determiners, the lead needed because of the delay of the bullet in getting to the target and the horizontal speed of the muzzle when the bullet exits.
The speed of the bullet is 1000 feet per second and it takes 1/7 second to get to the target. The horizontal component of the nickel's speed is (let's say) the sine of 28 degrees times the speed of the target that is a little less than half of 44 ft/sec , call it 21 ft/sec. 1/7 of that is three feet, the calculated lead due to the interaction of target speed and time of flight of the bullet.
But the muzzle is moving too, and that speed has been estimated here in ranges from very little to 18 ft/sec, though I thought the latter was a least five times too high. Let's say 3 ft/sec and that takes 3/7 feet off that first required lead so it's now two and a half feet.
Now these are fixed numbers and not influenced by the direction, right or left, of the angle of the target, except gun speed might be a little different but we've shown that it's a minor effect, accounting in this case for no more than 1/5 of the total lead. So if swing speed to the right is as much as 50% slower to the right as to the left, we are still talking about no more than 3 inches and I don't think people who hold this theory are talking about three inches.
So in the case of actual lead, I think the answer is "myth" for most of us who don't aim to within three inches.
Perceived lead is quite another thing and has little to do with the math we've just done. That's mostly illusion since the command "fire" has to have been sent well before the sight-picture looked right, assuming we are "swinging through the bird from behind" as most of us are. I hold little hope of ever figuring it out to any degree of accuracy and if people tell be they see it differently, I take their word for it, keeping in mind, however, that there's "really" no required difference.
Neil