I don't get what's so complicated about it. It's very simple. Lawful/Chaotic isn't related to society, the state's law, order, anything like that. Well, it can be, but that is obviously up to the individual character.

A lawful character acts in a way that is dictated by consistency, predictability and reliability. They belief in a code, a set of rules, a law, the law or anything similar. If you are familiar with this code/law/etc, a lawful character's actions can be foreseen accurately by others, because of their adherence to this code/law/etc. A lawful [good] character can be the stereotypical holy paladin who fights for honor, righteousness and the good of the people. He will never compromise his own set of rules, his religious rules, or the state's law. A lawful [evil] character can be a hired killer, who is only in it because of the money, and because he enjoys killing - and yet, he has his own set of rules, that no amount of money could bend. Maybe he doesn't kill women and children - not because of the nobility in his heart, but simply because he doesn't see it as a challenge, or because he doesn't take any pleasure it it. Maybe he is part of a brotherhood of assassins as well, and this brotherhood has it's own code that he would never compromise, not even in the face of death.

A chaotic character is the opposite. Their behavior is spontaneous, erratic and volatile. It is unpredictable and inconsistent. They don't follow rules, they follow their heart. A chaotic good character does what he feels is best to bring change for the better - one day, this might mean helping people on the streets by giving them food and water, and the following night he might be dressed in all black, throwing a firebomb at the tyrannic guard's barracks. He doesn't have a set of rules; one day, nothing is too extreme, the other day, everything is. A chaotic evil is very much the same, but the absolutely only thing he is interested in is himself.

In my opinion, Good and Evil are the two aspects that relate to society, not Lawful or Chaotic. Lawful and chaotic are completely objective things; Good and Evil are subjective - those two are in relation to society. Of course, there are character's whose moral views are different than those of society - this does not change their actual alignment, it just changes what they think their alignment would be. The deluded Tyrant who truly believes what he is doing is for the better of the people might think he is Good, but he is still evil.