After I left Christianity, I slowly lost the revenge/retribution form of “justice” that was taught to me. I don’t believe in capital punishment in the sense of execution.
Jail time, fines, and community service would still be useful sentences for deterring crime and for repairing damage done by criminals.
I think that killing criminals is a very dangerous thing to do because it is entirely possible for a person to be framed and convicted of a crime they did not actually do. Even if you know you have the right person, killing them does not help the victims of their crimes. Make them repay the individuals or families through financial means. It doesn’t fix everything but it is better than nothing.