Do I oppose the death penalty for conservative reasons?

I'm against the death penalty not because I think it's too harsh and cruel, but contrarily because I think it's not harsh enough, too merciful. To me, killing a murderer is like putting them out of their guilt and misery. I think life imprisonment is more severe than the death penalty because it forces murderers to go through the rest of their life thinking about what they've done. I think a constant reminder of a murderer's crime in a living hell is the kind of punishment murderers really deserve. I know it's supposed to be a liberal stance to oppose the death penalty, but if I oppose it for these reasons, isn't that conservative?