The logic behind the metaphor is this: since we owe everything we are--our very existence--to the workings of nature, nature is seen as moral. In short, over history, natural hierarchies of power emerge. Since they are natural, and nature cannot be immoral, traditional hierarchies of power are moral.
I would have hoped that merely writing that would have raised flags about whether it could seriously be as common as Lakoff is committed to saying it is; but apparently not. Let's consider an example of Moral Order discourse; say, Martin Luther King, Jr.'s appeal to 'the higher law'. This is very clearly discourse that fits under Lakoff's 'Moral Order' metaphor: it recognizes a moral hierarchy, it explicitly draws on natural law theory, it places a rather hefty emphasis on people keeping their place in the overall order established by God. But, of course, the inference from this is not that "traditional hierarchies of power are moral" but that any human hierarchy of power must be held accountable to higher principles, and that usurpation of power over one's fellow human beings is immoral.
The problem, I think, is that Lakoff treats two distinct forms of discourse as if they were the same thing. Genuine Moral Order discourse posits a moral order, an order to which everyone is accountable. It is not a hierarchy of power, it is a hierarchy of authority; your good lies not in respecting those who have more power than you do, but in making your function in society one that is consistent with an ideal order which society imperfectly approximates. He conflates this with a very different type of Order-based discourse, one based purely on retaliation: those who get uppity get put in their place. Now, it's certainly true that the two both use similar terminology on occasion -- the phrase 'law and order', for instance -- but we are supposed to be talking about cognitive structures and the uses to which the two are put are radically different, as different as Socrates and the Sophists, or King and the white moderates, or natural law theory and realpolitik.
And here is one place where I think we run up against a major weakness in Lakoff's attempt to apply his understanding of conceptual metaphors to politics. When we look at conceptual metaphor as a cognitive structure, as Lakoff does when he is just talking about the basic account, we find that it's actually just that: structural. So, for instance, to take one example Lakoff uses, we reason about love by using the metaphor Love is a Journey; love in such a metaphor becomes like an enclosure (we fall into it or fall out of it), it moves (it's not always the same), it suggests a destination that can't be reached immediately, and you can treat difficulties lovers face as impediments in this journey. These aspects of the metaphor structure our reasoning about love. Clearly there are stable correspondences here: love is a vehicle, the lovers are moving in it, they are overcoming impediments in a purposeful way, just as you would on a journey. But while this constrains the sort of specific content you can use, it doesnt actually select it for you. John and Marcy may see disagreement about how to educate their children as a major impediment on the journey; but Rosa and Rob will likely have radically different impediments to list. If I may use a metaphor to talk about how metaphor works on Lakoff's account, metaphors are like a set of boxes; in a Love is a Journey metaphor you have one box, the vehicle, already filled with 'love', and there will be box for the destination, a box for the obstacles in the road, etc. These latter boxes, however, will not come ready-filled; you fill them as you go, by throwing something into them as it comes up. Any sort of difficulty can be an obstacle in the road; the same difficulty will be for some just a little bump, and for others an almost insurmountable obstacle. When we think of the love of that couple and this couple as a journey, we don't think of them as the same journey. The structure of our reasoning about them will be the same; but the content that fills out that structure will vary according to circumstances. Lots of different people can have lots of different positions based on Moral Order, depending on how they fit the metaphor to their circumstances.
However, when Lakoff applies his account to politics, he forgets this entirely. The metaphors come with ready-made content. Moral Order on this treatment is not just a conceptual structure, it is an entire political position: "God above Man, Man above Nature, Adults above Children, Western Culture above Non-Western Culture, America above other nations, Men above Women, Whites above Non-whites, Straights above Gays, Christians above Non-Christians (or majority religion over minority religion)" (p. 99). Metaphors are now not merely inference-constraints; they dictate substantive conclusions. Some metaphors, those suggesting obedience to authority, are conservative; others, those suggesting empathy, are progressive. We get a really bizarre example of this in the chapter on "bad apples". One bad apple spoils the barrel, we often say; but if you're progressive you shouldn't, if Lakoff is to be believed. If we were really thinking of the Bad Apple metaphor as a conceptual metaphor, then just about anything could be identified as a Bad Apple under the right circumstances. But for Lakoff in The Political Mind the metaphor is not just a cognitive structure, it's a procedure for scapegoating (to defend yourself, you find a scapegoat and claim that he was the one and only bad apple). This is a rather abrupt move, one that confuses metaphor as a structure of thought with a particular use of metaphor. It's as if you said that talk about public trust made you a Communist sympathizer.
Once we recognize that Lakoff slips back and forth between metaphors as cognitive structures and metaphors as placeholders for very specific positions and strategies, it's very interesting to go through the book and identify points of equivocation. Or, at least, it's very interesting for as long as you can keep up; they are legion.