There is a D&D tradition that perceives Chaotic to mean "random" (= Chaotic Stupid), and by contrast, Lawful to mean "ordered" (= Lawful Stupid).
However, the above two unhelpful definitions are inconsistent and logically irreconcilable with the other more helpful definitions elsewhere.
The better definitions are Lawful=group and Chaotic=individual, especially for the sake of a roleplaying game.
Except that this runs afoul of other definitions (another serious part of the problem). If Lawful = group, then the lone paladin fighting the good fight against a nation that legalizes slavery would instantly fall due to failing to uphold the common group identity. If Chaotic = individual, then Robin Hood and his Band of Merry Men--despite standing up to a tyrannical usurper-king and actively breaking laws on the regular--are axiomatically Lawful because they represent the Organized Rebellion.
Which is why I use the metric I do. Lawful is about legitimacy, justification, and setting clear policies which only change under duress (and always with caution and care). Chaotic is about flexibility, adaptation, and keeping all commitments as open-ended as possible (and always with an eye on the alternatives).
Chaotic people can form associations, even large ones, but these associations are fragile, particularly if they're large, because
everyone in them might potentially say, "Ah, sorry guys, this isn't working out for me, have fun!" Such associations tend to form where a natural, unforced, long-standing drive or desire overlays enough of the population in question that they all willingly stick around--if departing would consistently be worse than staying, then people will stay. Pirate ships, for example, would sign contracts--not because they had any affection for law, for example, but because it's really hard to be a one-man pirate, and really, REALLY lucrative to be one of the blokes on the ship when it sails back into port full of booty. (As CGP Grey put it in the "How to be a Pirate: Quartermaster Edition" video, "We have a ship, and a business, only by our
cooperation...and only if we can
keep it. But the incentive is great.")
And Lawful people can go it alone. Inspector Javert is absolutely a one-man legalism machine, having conflated
executing all laws as written with
being a good and noble person. In the words of the author himself (translated, of course), "And, withal, [Javert led] a life of privation,
isolation, abnegation, chastity, with never a diversion." (Emphasis added.) Javert lives a loner's life, having explicitly almost no connection to the rest of the human race (his only vice being that he occasionally takes snuff when offered), and his individual isolation and refusal to interact (or belief that he is not allowed to interact) with the bulk of humanity is exactly what permits his hyper-legalistic mindset to prevail. Javert is Lawful Neutral tragic villain, perhaps even antivillain, someone with explicitly laudable precepts who applies them with a dangerous zealotry.
Even if we don't consider a
broken Lawful mind, but rather a healthy (even heroic) one, it is entirely possible for a Lawful person to be the Only Sane Man in a group--or, in the example that most readily comes to mind, the Only Sane
Woman, Hermione Granger. She is of course a fantastically gifted student and witch, being both intellectually brilliant and supremely skilled with the use of magic. But she's also the voice of reason and the one who tries to instill ideas like discipline, responsibility, and upright behavior in her friends. She has a
deep and abiding passion for justice (likely the reason she was sorted into Gryffindor rather than Ravenclaw), and commits herself wholeheartedly (even in the absence of interest from both wizards
and house elves) to the cause of house-elf rights, founding S.P.E.W.; this very impulse tends to
isolate her from others who don't share her passion or don't think that systemic change is needed.
Lawful can disagree with group identities if those group identities are founded on unacceptable situations or principles. Chaotic can accept, even embrace group identity, if that group identity is founded purely upon sustained common interest, rather than arbitrary standards or someone else's rules.