He's going to die eventually, and he thinks he's going to paradise. Why not let him rot in jail for the next 99 years, i.e. no chance of parole.
Execution just brings him to paradise that much sooner. If I understand it correctly, it's going to cost society more to proceed through the death penalty appeals process, than it will to imprison him for the rest of his life.
He probably doesn't want to die just yet, but he would expect the welcome of a martyr in paradise. Just make him suffer in jail in a country he hates, and make sure he gets a news feed to keep the anger burning away.
In other words, give him the chance to realise he's wasted his life, and he's not getting to paradise any sooner. Such despair is a suitable punishment.
Besides, why are individuals punished for premeditated homicide, but it's OK for the state to do it? You're only reinforcing that it's ok to kill people (and yes, there are justifications for self-defence, whether on a personal or country-wide basis).