The various communal-farming, work-where-you-want communities (e.g. the controversial Israeli kibbutzim) may also be useful to look at, if you're wanting real-world analogues.
Beyond that, at least for me, the difference I see between "Lawful" and "Chaotic" values are as follows:
1. For Lawful folks (individuals and societies), having a clear process or procedure is important. If you're doing something well-trodden, it should be as consistent and principle-based as possible. If you're breaking new ground or rebuilding something, then the process should be well-documented and visible (LG would add "clear and understandable" as a goal, LN would probably focus on "efficiency" alone, LE would add elaborate "precision" for maximum exploitation). Chaotic folks care most about solving each problem on its own terms--tying yourself down even to a universal principle means you risk not being able to fully address the unique problems of each situation. As a result, chaotic solutions tend to be quixotic, sometimes even seeming contradictory, because they're almost purely about context and making a judgment call, which may vary from one case to another for subtle or ill-defined reasons.
On this axis, a Lawful society is somewhat more like the "civil law" structure, where laws are codified thoroughly, and exclusively, by legislators and judges "merely" establish facts and then determine what the law require, while a Chaotic society is somewhat more like the "common law" structure, where laws originate from legislators but get reviewed and interpreted by judges, leading to previous precedent that is generally only overturned when a case establishes a break in the context compared to the original.
2. Lawful folks have more "bright lines" they won't cross. It's harder to come up with things that a Chaotic person would ABSOLUTELY NEVER EVER do, no matter what. Thus, a Chaotic society is one where even particularly strong norms or values are always at least a little bit more inherently open to transgression. You see this contrast most strongly in LE vs CE, where CE is often portrayed as wild and unpredictable in its villainy, while LE is portrayed as the "magnificent bastard" alignment. Yes, both of them can and will do evil, but the Lawful Evil person can be appealed to on the grounds of Lawful limits, whereas the only thing you can really appeal to with the CE person is whatever personal goals they happen to have--there's no transcendent appeal you can make to something "beyond" the CE person and their goals. When considering LG vs CG, it's more fuzzy (because CG has stuff it won't do because doing so would be evil, but is otherwise usually pretty open to any method that "gets the job done"), but there's still a sense of something in there. An LG person doesn't just want to achieve good, they want to achieve it the right way; there's concern about legitimacy of method, honesty, being "above board," that sort of thing.
On this axis, a Lawful society is one where there are things you Just Never Do, whether because of explicit legal restrictions, or because of firm and well-known social norms. A Chaotic society is one where people do what is necessary to achieve their goals, even if it's transgressive or improper; indeed, the very idea of "impropriety" is a bit daft as far as a Chaotic society is concerned.
3. Lawful folks put something of a premium on being justified in their actions. That is, to do something, you must have a reason, one that is preferably as independent as possible from emotional attachments or the like, that is robust enough to stand against rational critique. There may be several things a Lawful person or society would like to do, but won't because they're unable to justify it. (Consider, for instance, the concept of casus belli, as it often appears in strategy games: you must have a reason to go to war, even if you secretly manufactured that reason yourself.) Chaotic folks...don't really care about justification, but rather about...I guess "sincerity"? Do things because you mean it, not because you can "prove" that you "should" do it. Better to be earnest and wrong, or to repeatedly contradict yourself, than to dance on pretense and deny the facts.
On this axis, a Lawful society is one where people build justifications, and attack the justifications of their opponents in order to try to stop them. A Chaotic one pursues goals because they desire them, and accepts shifting goals as merely being honest with yourself and others.
4. Chaotic folks see all authority as transitory or (ironically, compared to the previous point) in need of justification. For them, "authority" is a thing that cannot, even in principle, simply be "given"; it must be earned, and it can quite easily be lost. Being appointed to a position of power confers nothing; only by demonstrably using that power in ways a given person approves of can merit respect and deference. Lawful folks, pretty obviously, see this very differently; authority is to be respected unless and until it is abused, rather than distrusted until the holder proves worthy.
On this axis, a Chaotic society is one where authority figures--as others have noted previously--frequently shift and change, and as a result the members of that society tend to resist the imposition of authority unless they personally develop a respect for those who currently hold it. As soon a it changes again, though, the cycle starts all over. A Lawful society, by comparison, invests the holder of an office or title with an inherent respect,
You'll note that many real-world things don't consistently fall on one side or the other here. Frex, some folks might not really care about being justified, but might want clear and well-defined rules and procedures within which to make their spontaneous decisions. Others may sit on different sides of even a single axis depending on context or scale. E.g., you can have folks IRL who think all police officers should be respected immediately unless they do something really blatant and heinous, but who distrust distant high-level officals, even though these people may never have met either the police officer or the distant official.
