Contrary to popular opinion, natural law has nothing to do with "nature red in tooth and claw". Darwin's theory, whether true or not, has absolutely no bearing on natural law theory.
Natural law speaks to morality, the nature of sin and virtue. Darwin's theory says absolutely nothing about morality, sin or virtue. In fact, Darwin's theory does not even allow for value judgements. You cannot say something is "more evolved" or "less evolved", you cannot call one adaptation "better" or another "worse." You can only speak of whether or not an organism's chances of survival are greater or less, given the circumstances. That's it.
Apart from using the generic concept of a thing having a "nature", natural law theory also has nothing to do with pagan Greek thought. Natural law is a purely Christian concept that supports the purely Christian concept which is personhood.
For an example of how natural law works, let us assume two couples. Each couple gives birth to a sickly child. The first couple takes the child out to the forest and abandons it among the trees, where insects, birds, coyotes and other animals eventually eat the child (either eat the child alive, or eat its corpse, because the child died from exposure).
The second couple take their child to the NICU, where a team of doctors and nurses spend days hooking the child to machines, artificial pumps, artificial temperature control, etc., in order to assure the child's survival.
Which couple acted according to the natural law? Since God is love, and God is life, and we are made in God's image and likeness, the SECOND couple acted according to the natural law. They acted as God acts, assisting the little one in need. Meanwhile, the first couple acted contrary to the natural law by abandoning their child to certain death.
That's natural law. Natural law is not about the laws of nature. Natural law is about how men are meant to image, in their own bodies and their own actions, the very life of the Three Persons of the Trinity, the God Who Is Love and Life. Darwin simply isn't relevant.
Natural law theory rests on our grace-empowered ability to image God's life of love. If God sends the grace (and He does), then we can live natural law - we can live according to our nature. If He does not, then we cannot. Our rational minds need grace to choose the good, our bodies need grace to do the good. Without grace, as St. Paul said, I know what is good, but I do not choose it, rather, I choose that which I know is not good. Natural law does not work without grace.
Liturgical Christians know that the Fall marred human nature, but did not totally destroy it. In order to believe in the concept of "inherent human rights", America's Founding Fathers had to implicitly repudiate Luther and accept liturgical Christian understanding of human nature: marred, but not destroyed. Thus, if the Founders were correct about inviolable human rights, it is only because they implicitly refuse to accept total depravity. It is only because they embraced the Catholic understanding of human nature.