Even in non-liberal states, the death penalty has become a race between advancing age and the appeals process. As an example, here in Florida an execution was carried out just a day ago for a 1992 murder of the wife and rape & murder of a 10yo stepdaughter (22 years back). The (unworthy-to-be-named) murderer apologized to his victim's family before the execution was carried out by lethal injection(s).
Is it justice to wait 22 years for a penalty to be carried out? I cannot see it as being so and wonder if life imprisonment is a harder sentence if assured there is no parole. It certainly would be less expensive for the taxpayers.
The appeals process is designed to give the convicted murderer decades to appeal and delay the executioner. Tennessee has a death penalty but rarely carries out executions. Death row inmates have a bigger chance of dying of old age or disease than execution.