Bruv the goal is telling you the plain fact that it costs a dramatically greater amount of money for the state to murder someone than to put them in a cage indefinitely. What is your goal?

And life in prison isn't more just. Nothing the American carceral system does is justice. But if you're alive then at least it gives you time to prove that the cops who fingered you were lying about everything and try to get a new trial. Though even that doesn't work sometimes thanks to our august and venerable supreme court.