I'm reading a book called Marcus Aurelius and the Later Stoics by F.W. Bussell, one of the many books which are freely available through, and which I freely download on, my nook, and a sentence of his to the effect that theology without anthropomorphism is Natural Law, "got me thinking" as we like to say.
As far as I'm concerned, the fact that so many of the religions we've dreamt up during our relatively short time on earth ascribe very human traits, and even sometimes forms, to a deity creates problems for their credibility. Among these problems are those associated with the idea that a supreme being came to live among us, and those which assume that such a being finds peculiarly human conduct or misconduct of great and indeed paramount interest. For example, for me at least, it's difficult to believe that God is very troubled if we have sex out of wedlock, and even more difficult to believe that he punishes those who do eternally.
"Natural Law" can mean different things, in ethics and in law. But one of the things about stoicism I find interesting is that it considers human nature, and nature generally, in coming to certain conclusions regarding good conduct and the good life. In coming to these conclusions, it doesn't necessarily rely on the existence of a transcendent and bafflingly human God functioning as law-giver, although it does maintain that there exists as a part of nature a kind of Divine Spirit or Reason in which we as humans share. Bussell (and others I've read) seems to feel that the later stoics began to think of this Spirit, or Reason, or Logos as transcendent and personal, and I know that Epictetus, for example, would sometimes refer to it in a personal manner (i.e. as if it were something like a person); but I'm not so sure.
Be that as it may, I'm personally sympathetic to the view that we humans generally share certain characteristics which can be identified and described through the use of our intelligence, just as the rest of nature has characteristics which can be identified and described through the use of that capacity. If that's the case, it would seem to be possible to use that information in making certain reasonable inferences regarding good conduct and the good life, based on what most of us find desirable (there will always be people who want or at least will profess to want to kill and torture other people, or who are insane, but I don't think their existence precludes us from making such inferences any more than "freaks of nature" or highly unlikely but still possible results prevents us from coming to scientific conclusions as to probable outcomes).
Such inferences could result in certain non-absolute rules, and to the extent that they are based on human nature and the place of humans within nature might be considered something like Natural Law. Unlike Natural Laws, however, those rules need not be conditioned on a belief that that they exist in some fashion separate from us, or are imposed by some transcendent higher power. They cannot be separate from humanity or from nature as they are derived from both--from the intelligent consideration of humans as they interact with each other and their environment.
So, perhaps Natural Law theory if broadly defined can have a naturalistic basis, one independent of the need for God as traditionally conceived.