I used to like the D&D alignment system which had a chaotic/lawful axis separate from the good/evil axis. I think the reason I liked it so much was because it seemed to add something less debatable; if we couldn't agree whether a character or action was good or evil, we could probably at least agree on whether it was chaotic or lawful, even if we didn't agree on the relationship the two axes had. After a while I got disillusioned with the system and no longer use that language (outside of my talk about the strawman chaotic evil trope, which I think is an appropriate use).

It doesn't actually make things any less open to interpretation. Two people can mean opposite things by lawfulness and neither can be wrong.

First of all, it's a red herring that lawful characters are necessarily in support of established authoritites. Some people interpret it that way (the easydamus article says it a few times), but others say that lawfulness only means believing that it would be better to have some established authority, not that the present ones are good or deserve loyalty. Here's some people arguing about it. Still others say that lawfulness doesn't have any intrinsic association with authority, just strict adherence to a clear set of principles; hence a libertarian purist like Shane Killian would be highly "lawful" despite being an anarchist. Although, when you think about that, it becomes more like "philosopher versus non nonphilosopher".

A common aspect of interpretation thrown into it is that consequentialism is a chaotic idea, while lawful characters adhere more strictly to "principles". But it's also said that chaotic characters are more individualistic; this is already at odds, because consequentialism inherently has collectivist implications (if you can sacrifice one good for another, you can sacrifice one person for another - the TVTropes article pretty much makes that point itself).

Some people will say that lawful characters "hate to see the guilty go unpunished", but many also say that "thou shalt not kill", or in general the modern Christian opposition to retribution, is a lawful idea. Both of them can be framed as strict adherence to one's principles.

The D&D two-axis system clarifies nothing, it only adds a meaningless dimension that causes at least as much confusion as the other one.