The problem with “life imprisonment” is that (1) there’s always a chance a judge will release them, regardless of the original sentence, and (2) they can still harm others while in prison. On the other hand, a BIG problem with execution is that the person may not be guilty, and another is the possibility that a person may repent and be converted.
This is why I say it’s not an easy question.
I read an article years ago by a priest whose rectory was a block from a state prison. He was called in whenever there was an execution. He said that every man executed there, for decades, died repentant, while most of the prisoners who were NOT facing execution were NOT repentant.
IIRC, the problem of executing the innocent is non-existent.
I agree.