Recidivism rate is high so People who commit murded will likely commit other crimes if released so removing them from society is a good thing. Keeping them in jail forever is a waste of resources so execution is right approach. The one thing is that process should not take 20 years and all appeals should run out in a year or two at most so justice is reasonably swift.
We should not torture them on purpose but besides that I do not particularly care if they suffer or not during execution.