According to Natural Law, the right thing to do is that which accords with one's nature. But what if something really nasty accorded with one's nature? This is, of course, akin to the objection to divine command theory from the question "What if God commanded something really nasty?" Both theories can give the same answer: "That's just impossible." God couldn't command something really nasty and there just are no possible natures of rational beings that require such nastiness. As far as that goes, this is fine, though at this point in the literature there are two more steps in the dialectic to think about.
I want to, however, consider a side-step. Why is it impossible? One could think this is just a brute and unexplained impossibility, but that is unsatisfactory intellectually. Even apart from the Principle of Sufficient Reason, we don't like brute facts that look like too much of a coincidence. And it looks like too much of a coincidence that all of the nasty cases are impossible. We want an explanation.
The divine command theorist has a pretty immediate explanation. We're talking about God's commands, and necessarily God is perfectly good or, if one prefers, perfectly loving. (Of course, those divine commands who want to define the good, and not just the obligatory, in terms that involve divine choices cannot give this answer. But so much the worse for that version of divine command theory.)
I think the Natural Law answer can be similar. A nature is an essential (in the medieval sense, maybe not the modal sense) mode of participation in God. It's impossible for a rational being's essential mode of participation in God to require nastiness, because of the nature of God. (Why is God's nature that way? Maybe here we have a brute necessity. A single brute necessity is much less problematic than a whole slew of them. Or maybe we can talk of God's perfection here.)
So there is an explanatory gap that Natural Law points to, and bringing in God closes that explanatory gap. Are there other ways of closing that gap? Maybe. One would be a heavily Platonic theory on which natures are modes of essential participation in the Form of the Good. The Platonism here would be more like Plato's own Platonism than our more anemic contemporary Platonism. The participation relation would not be exemplification as in contemporary Platonism, but something ontologically meatier, more like the participation in the theistic version of Natural Law.
In any case, the question of why something nasty couldn't be required by one's nature points towards serious metaphysics.