It's the other way 'round, actually. Murder is homicide that is not: sanctioned by law, including legal acts of war; or justifiable (in self-defense or in the defense of others, usually subject to a "reasonability" requirement).
Let's get this much straight: no matter what side of the fence you come down on in moral terms on the taking of a life, much of what is being bandied about is based on a false premise, that being the natural right to life. It is, as they say, "a fond thing, vainly invented".
In order for human society to work, that society must, for its own preservation, constrain the acts of individuals, and impose sanctions to enforce the prohibition of such acts as might destroy it. Humans are fundamentally social creatures, essentially defenseless and doomed to extinction without the transmission of culture and technology through society. We live together or die separately (and remember that whatever tools you were envisioning to enhance your chances of survival, you either acquired or learned of through the work of others). Thus we need to have prohibitions against things like people killing other people on their own say-so. If we had to fear death every time we accidentally ticked somebody off, we wouldn't be spending a whole lot of time in one another's company, would we? With neither claw nor fang nor great strength nor speed, we wouldn't have lasted very long as loners.
That prohibition against murder (unsanctioned killing of another human being) can be rightly called a "natural law". But it does not logically follow that if I am prohibited from killing you under most circumstances that you have some fundamental right not to be killed under any circumstance.
If there is a moral issue involved in capital punishment, it is not based on something the guilty possess, but rather what we who sit in judgement possess. We, as a society, decide to sanction a killing or not based on our own values, not on the "rights" of the convicted party. If a society sanctions killing in retribution (which is the only righteous justification for punishment, as C. S. Lewis so eloquently stated) then it is not murder (by definition). If it does not--if it considers some other retributive measure more appropriate--then the question is moot.