Physics is the law, everything else is a recommendation.

Everyone has rights until they vaiwe them by infringing on others rights.
That includes the right to life.
God is merciful.

this is a great question!

my conscience says it is. but also I dont really know what to do with pathological killers otherwise.

take a play out of the uk's book and create a penal colony on mars?

Can a human institution override Natural Law?

You made it say as if "Natural Law" wasn't invented by man. It is. Maybe it's more ancient/low_level/basic but still it's invented by man. Similarly institutions/goverments and constitutions are invented by man.

And as both are man-made I don't see any contradiction by one overruling another. It's just a convention we made up.

What if the person is innocent?

That is the problem with death penalty. It's an ultimate tool to silence inconvenient people forever.

Without death penalty if you set up someone and send them to jail (think dictator states) you risk getting exposed somewhere in the future. It introduces some back-pressure to the oppressive state.

And that is the reason why I am against death penalty. It's just a too powerful tool for dictator wannabes.

Portugal was the first modern country in Europe to get rid of the death penalty. We don’t even have life sentences, the max here is 25 years. But honestly, there are some crimes so bad that even the death penalty feels like it's not enough. Some people deserve worse.

Is Capital Punishment a Violation of Natural Law?

Natural rights are inalienable.

Is life imprisonment a more humane and morally sound alternative?

It also goes against natural law. It's hard to conceive of this in the world we live in, but the ideal is exile as punishment, refusing to make deals with those individuals. If they succumb, that's their problem.

I oppose the death penalty, with the possible exception of those who have confessed to committing heinous crimes.

That’s because we don’t have sufficient certainty in establishing guilt though.

I have no ethical qualms about the death penalty in principle for certain crimes.

I used to think there are some people so bad it makes sense to kill them but then I know the government sucks at everything so it's probably stupid to give them this power

Let me quote the following:

From a Reformed Christian worldview, the death penalty is not a violation of Natural Law; on the contrary, it is an expression of justice grounded in the holy and just character of God.

Natural Law is not something autonomous or separate from the character of God. What is "natural" is not defined by social consensus, but by what God has revealed in His Word and what He has inscribed on the human conscience (Romans 2:14–15). Human life is sacred because man was created in the image of God (Genesis 1:27), and that is precisely why murder—the act of violently taking away that image—demands the death penalty.

After the Flood, God clearly established in the covenant with Noah: "Whoever sheds the blood of man, by man shall his blood be shed; for in the image of God He made man" (Genesis 9:6). This is not a temporary Mosaic law, but a pre-Mosaic moral principle that remains in force. Capital punishment, when applied justly by a legitimate authority, is not personal vengeance, but justice delegated by God to the civil magistrate: “For he does not bear the sword in vain, for he is God's minister, an avenger to wreak havoc on the wicked” (Romans 13:4).

The modern objection that capital punishment is “state-sanctioned violence” ignores that the authority of the state is not autonomous, but derived from God himself. If the state acts within its moral and legal jurisdiction, its use of the sword is not a contradiction of the right to life, but a defense of it. The right to life is not absolute in the case of the murderer, because he has irremediably broken the moral order. It is not that the state denies the value of life, but rather affirms it by severely punishing the act that most degrades it.

And if the person is innocent? This is a good question that requires a "fair, prudent, and sober" judicial system.

But abuses or errors do not invalidate the moral legitimacy of capital punishment, just as medical errors do not invalidate medicine as a science.

Finally, the alternative of life imprisonment is not morally superior. In many cases, it is a form of prolonged suffering without final justice, or, even worse, it can communicate that the crime of taking a human life does not deserve a proportionate response.

The only fair “punishment” is reparing the damage done. I don't see how capital punishment does that.