Execution shouldn't be an option. At least with life in prison you can release a person if you fucked up, with significant financial compensation for their time in prison. You can't un-execute a person. The state isn't competent enough to be given such power. Nobody is.
Giving the state the power to take life from its citizens is open to abuse when the wrong person gets into power. Not allowing it in the first place is how you go towards stopping that sort of thing.
We don't seem to have a problem giving the state power to take life from other countries' citizens, though. The only way you can stop that is if the other country is more powerful than yours.
But what is the cost of compensation for executing somebody that was likely innocent?
—Think about this. Life in prison is cheaper than an execution If the convict serves their entire sentence. –Is it still cheaper if the inmate has their conviction overturned and subsequently sues for restitution?
I genuinely don't know the answer to the latter question but nothing about sanctioned executions sits right with me.