Suppose a convicted serial killer is sentenced to natural life in prison without parole. While in prison the killer manages to fabricate a knife and kills a prison guard. There is no additional incarceration that the justice system can add to the killer's sentence. If the death penalty is used in this case, I would consider it justice, not revenge.
That is an interesting case you bring up and I would agree with you in this particular case. In order to keep society safe, we would need to kill a person like that.
For the most part though, the death penalty is just government sanctioned revenge killing. I can see how that could be fine in really heinous cases like the rape/murder of the PT student in India(where the death penalty was used after a long time) or the Boston marathon bombers, but the death penalty really needs to be used much more selectively than it is today in America. It should not be used for every random gang member who shoots another gang member.