Radical socialism is chaotic good. It conceives of some good (the equalisation of material shares and abolishment of capitalism) and is fairly explicitly comfortable with subverting legal norms or using extra legal measures to achieve this if such measures would be effective. The rule of law, after all is just more bourgeois ideology. Ultimately, the state is supposed to wither away, so there is no way they are any form of lawful.

Slightly more orthodox Marxists might be chaotic or true neutral since they are sceptical of all ideology. They don’t see communism as necessarily good, just inevitable.

Libertarianism cannot be lumped under one umbrella. Anarcho capitalists are plausibly chaotic neutral because of the anarchism. But dnd rules allow that the lawful component can be fulfilled by adhering strictly to non-legal codes. So, since anarcho capitalists claim adherance to the non-agression principle, they can be put under lawful neutral if such a move is available. (it would be a mistake, I think to split the difference and make them true neutral)

Rawlsian (or for that matter any other anti-perfectionist) liberalism is especially lawful neutral. It very explicitly eschews appeals to any conception of the good and tries to stay neutral between all conceptions of the good.

Movement conservatism and movement progressivism on the other hand all conceive of themselves as using the law to achieve certain substantive goods. As do all other perfectionist accounts of justice. (e.g various forms of communitarianism, forms of liberalism and (non-anarchic) libertarianism that view autonomy as a substantive good to be realised) Depending on how you evaluate their goals, you have to place them either in the Lawful good or Lawful evil category. If you allow that the ideology gets to define what is good, then all of the rest go under the lawful good heading.