Absolutely. When you sentence someone to life in prison without parole, and they continue to commit capital crimes in prison, they deserve to die for it. Why should we keep someone around who was imprisoned for life for such crimes and then have no means to punish them for doing those crimes in prison?
Why should another inmate, or a guard, or staff, in a prison be subject to rape, murder, or the like by a prisoner who knows they will suffer no consequences for their act? Solitary isn't punishment for someone like that. It's simply an attempt to minimize that prisoner doing it again. Note, that won't stop them entirely and they could still commit further crimes. Death is the only sure solution.
There are also crimes so heinous, so vile, that they deserve something more than simply putting someone in prison for life. Without a death penalty what would you give such a person, multiple life sentences without parole? How stupid is that? Hell, such a person might take it as a challenge to see how many they can rack up.
The death penalty is a deterrent, an absolute deterrent, that prevents the person put to death from committing further crimes.
Without a death penalty there will be those in our society that see they can spend their life committing murder, rape, or whatever, be it in prison or on the street and face no penalty for their actions. Eliminating them from society by death is the only sure option open to dealing with such a person.