Here is a practical example to try to illustrate the difference: in the framework of the AD&D alignment sections, the LG person has as deep a disagreement with the LE person as with the CE person, perhaps even moreso, because they disagree radically over whether social structures are a source of welfare or just a yoke upon others.
I would assert that you're viewing that the wrong way. Both the LE and the LG character believe that clearly-defined, principled restrictions are for the "good" (read:
betterment, NOT
righteousness) of society. But they have deep--fundamentally deep--disagreements about
which restrictions there should be, and what
specific principles those should follow. Both the LE and the LG are fully committed to the idea that a society with specific, and inviolable, rules is fundamentally "better" than a society without them. But "better"
to what end--that's where they disagree.
Meanwhile, LE and CE agree that the concept of "human rights" is bupkis, and that there is no more philosophical requirement to respect the "dignity" or desires of others than there is a philosophical requirement to wear orange and sing the can-can. The only thing that matters, values-wise, is whether you are able to get what you want out of the world; you don't take what you can get,
you get what you can take. But they fundamentally disagree about how you go about that. LE says that the strong control, and are served by, the weak via the exercise of authority and discipline; although the strong (generally) must still make effort to maintain their position, it is theirs by some external
right or
justification. CE says the strong control the weak purely through force and fear (fear of this battlestation). The strong retain power only as long as they can defeat those who would challenge them; if they can be beaten, they obviously weren't strong enough, and thus didn't "deserve" the position they held nor the tribute of those weaker than them.
This, incidentally, is why you see a serious tension (also revealed in that same "fear of this battlestation"/"I find your lack of faith disturbing" scene) in the various Empires that the Sith have constructed. The Sith philosophy is fundamentally Chaotic Evil. The student only remains student until the balance of power shifts in their favor (why the master takes true apprentices at all is, IMO, not particularly clear--though you could argue it's a prestige thing, "I'm so strong, I can keep *this* clown in line!") But the Empire is, essentially, a fascist state--regimented, organized, hierarchical, instilling blind obedience to commands rather than relying on the coercive power of force (heh) and fear. Hence why you see antipathy between some of the moffs (not Tarkin, obviously, who is very much Neutral Evil) and Lord Vader, with the latter
literally being at the throat of one of the former. This becomes
painfully obvious in SW:TOR, if you play as the Imperial Agent; the degree to which the chaotic, meddling influence of the Sith Dark Council stymies Imperial Intelligence, even causing outright and severe damage to the military and political infrastructure, is utterly
insane. An Empire ruled purely by its bureaucrats would be a billion times more effective than the one ruled by Sith, but the Force is so strong (both in terms of manipulating minds, and in terms of brute force) that it's difficult or even impossible for the non-Force-using population to assert control.
Whereas once you hold law up as a distinct value, then the LG and LE person have some value in common. That's the thing that I think is incoherent.
I fundamentally disagree. LG and LE think social groups fundamentally
need to be organized in order to accomplish anything meaningful. That's a value agreement right there. What counts as "meaningful accomplishment" is where they differ. Slavery is perfectly fine under LE, because it can achieve
results if properly managed. Similarly, concepts like
droit du seigneur, punitive taxes, secret police forces, and torture are all in LE's wheelhouse, as long as there is some kind of "justification" for it (though it may be contrived). Lawful Good, on the other hand, has to balance a number of concerns like respecting rights, improving general welfare, etc. just as you said. LE doesn't give a crap about *welfare*--they care about *productivity* and *efficiency.* Which might mean doing things to improve welfare--but not because welfare itself is good, merely because it is a means to an end.
Or, to put it a different way: Good sees people as ends, and thinks that treating people as a means to an end is The Most Terrible Thing. Evil generally doesn't see people as ends, and thinks that it's idiocy not to treat people as means if that can get you what you want. Law and Chaos, then, are merely about
how you go about treating people as ends or as means.