Adam Lanza was unable to legally own firearms. He obtained them illegally. Since you have no solution on getting rid of illegally possessed firearms, you won't stop people who want to get them for crimes. If someone is willing to commit murder, they will not care about your silly gun ban.
But they still CAN obtain these weapons if you ban them because criminals won't turn in their firearms. You ban solves nothing but to remove those who don't commit crimes from being able to defend themselves. That is, unless, you have some grand plan that gets criminals to turn in their firearms. I'm still waiting for your solution on that one.
And if AR15s were illegal at the time then Lanza's mother would not have one for him to steal. You seem to keep missing this simple logic.
A ban makes it harder for murderous nut jobs to run out and buy one. I've now said this a dozen times and you still don't understand this basic logic. Or maybe you do and just don't want to admit it.