Well, I think imprisonment is cruel and unjust, but aside that, you and I have already agreed that killing someone in self defense is just, and you haven't actually responded to my reasoning at all. You're reiterating your position, which is fine but doesn't lend itself well to fruitful discussion.

A jury, the state, all that I can agree with. That doesn't mean though that a group putting someone to death is always unjust, just that our mechanisms for doing it are.

I'd argue that me and my buddy deciding to go grab someone and kill them for, say for example, killing my cousin or raping my nephew or threatening to do so is entirely just.