Well, you've got nothing even close to what I'd vote, Jack.
Personally, the definition that I've found makes some sense, is reasonably internally consistant, and is usable (require the other two) is that Lawful tends to think in terms of groups, while Chaotic tends to think in terms of individuals.
That isn't to say "what's in the group's _best_ interest" (that would be LG), but "American, German, Chinese" or "Democrat, Republican, Libertarian (aka 'nutjob' to a Lawful)". Chaotics also don't think "what's good for _me_" (that would be non-good), but "Bob", "Sue", "Sven".
Because Lawfuls deal with large grains (groups), they seem better at organizing things. And they are -- putting people into boxes is a great way of getting things accomplished in the short term. Chaotics, dealing with many small grains (individuals) seem very disorganized. Again, they are -- it's much harder to figure out what Sven is doing than it is to figure out what the majority of Swedes are doing.
Lawfuls can appear inflexible because it takes some time to figure out which box things fit into, and they may try to put square pegs into round holes. Chaotics are flexible because they approach every situation as something completely new.
Unwise Lawfuls can fall into sterotypes and prejudices -- "All orcs are evil", "All slaves are better off serving", etc. Unwise Chaotics can be shortsighted, forgetting about the ties a foe (or friend) may have -- "I kill the diplomat for his rude remark."
I think it works well with most of the stereotypes. It also keeps down stupid quandries/types like the Paladin following the obviously evil law and Chaotic Neutral being certifiably insane.