As a counter-point, where in the US has any law stopped teenagers looking at naughty things on the internet?
The data proves nothing about whether it works because it's a cultural problem far more than it is a means problem. They choose to go out in a blaze of infamy rather than be a nobody. They generally are planned long in advance, there's plenty of lethal things they can get their hands on.
1) Many sources seek to inflate the number of school shootings by counting incidents in which the school is only incidental, not the target. Think drug deal in the parking lot when school is out etc. And note that counting firearm deaths to minors counts mostly gang vs gang stuff.
2) It is almost certain that guns save more people in self defense situations than they take in all mass shootings (using the realistic test of public and indiscriminate targets--again, the numbers are inflated by things like gang fights), let alone just school shootings. (And, no, I do not believe Lott's numbers. He's way high and an awful lot of what he does count is deterred robbers and the like, where death was unlikely in the first place.)