Proving guilt beyond all reasonable doubt won't happen with mob law. You will see innocents killed.
Of course, that makes all of the mob killers too and they are then targets themselves. In my background of sectarian violence, this is a very familiar scenario. Its hard to see the point of the NAP if that is how its intended to work.
Ahh. I see your point, and indeed, if the mob decided to take vengeance, that would tend to break the system. Thus why I disapprove of retributive violence. It's usually counterproductive, and always unproductive. In other words, it never fixes anything, and usually makes things worse. The solution here is again, since nobody is in immediate danger, to use arbitration. Each of those people have a grievance against the killer, which can be brought to arbitration.
He's harmed someone, violently, so in this instance, I would consider forcing him to show up justified.
A system where a mob can hang a man without a jury trial is a system where mobs will hang men without jury trials. If the mobs are of different races or religion, they will argue its self-defence. The question is whether the NAP forbids it? If not, its a lot less benign that I thought.