Accounts of moral obligation often have broad analogies to accounts of laws of nature. This is not very surprising, as despite their differences they are both strong modalities (Box) and they both have to accept the basic D axiom (Box implies Diamond), since moral obligation (Box) has to imply permissibility (Diamond) and laws of nature (Box) have to imply physically possibility (Diamond). It doesn't seem to be much considered, though, although I am pleased to note that Reutlinger, Schurz, and Hüttemann in their SEP article on ceteris paribus laws of nature at least briefly recognize that there can be a link of some sort between ceteris paribus laws of nature and prima facie norms.
It's common to classify accounts of laws of nature into two rough groupings: Regularist or Regularity (sometimes called, a bit controversially, Humean) accounts and Necessitarian accounts. On a Regularist account, laws of nature are, as you would suspect, just regularities. The Boxiness of the laws of nature is temporal: they are just things that always happen, according to some measure of what counts as 'always' (i.e., according to some kind of regularity). Necessitarian accounts take laws of nature to identify necessities in a stronger sense than this. The basic difference, in other words, is that Necessitarians want to say that you can have regularities that are not laws of nature -- that there are things that happen always that could be otherwise than they are, and these have to be distinguished from the fundamental laws of nature, which in some way have to be what they are.
The analogy between deontology and nomology holds here: we can classify accounts of moral obligations into two rough groups, one of which clearly has affinities with Regularist accounts of laws of nature and one of which clearly has affinities with Necessitarian accounts of laws of nature.
Regularist accounts of moral obligations are most commonly associated with consequentialists: moral obligations for consequentialists are regularities, things that happen to be always better, according to some practical measure of 'always'. Despite the association, I don't think Regularists about obligation have to be consequentialists. The reason for the association is that a Regularist needs there to be something morally significant for obligations to be the regularity of, and consequentialism is the most popular and influential theory that has an obvious candidate in how it conceives of consequences.
Necessitarian accounts, on the other hand, are most commonly associated with deontologists. As in the prior case, I doubt this is a strictly logical connection. The reason for the association is that Kantianism, the most philosophically influential deontology, is founded on an attack against any and every kind of Regularist account of obligation; this is precisely what Kant is doing in the early part of the Groundwork.
Likewise, one can see that objections to this or that nomology often have counterparts in objections to the analogous deontology. Deontological Regularists hammer Deontological Necessitarians on epistemological worries just as hard and as often as their nomological counterparts hammer Nomological Necessitarians on them. Issues of idealization and precision show up in Deontological Necessitarian attacks on Deontological Regularists just as often as they do in the Nomological Necessitarian critiques of Nomological Regularism.
Occasionally there are accounts of laws of nature that don't fit easily into the Regularist/Necessitarian framework (accounts that focus on natural classification, for instance); it would be interesting to see how these analogize to accounts of obligation. And a further issue of interest would be differences; different interpretations of Box and Diamond make different modal axioms more plausible or less plausible, and this would affect how the analogy works.
