What makes you so sure it's just mans justice? Does God say let the repeated offender thief go with no punishment? I seriously doubt it, so how much less repeat murderers? It's the natural order of a very sensible law, and yeah, mans law, the law the bible says God has his hand on, and for good reason, to punish for the sake of stopping the offender, as well as justice, especially in cases like we are talking about.
Or, how do you think God stops people like ISIS...lightening/loving them to death? Or does he expect good people to not look the other way?
So just maybe your "bad bad Christian" comment is not quite accurate.