Also of note, in traditional DnD, characters of "lawful" alignments were more concerned with society as a whole, and how their actions affect the whole, rather than the individual. Lawful characters are always willing to sacrifice a few for the benefit of the whole. It's why they are good with systems, and why they like rules, because rules (laws) are used to control individuals so that the individuals will fulfill their duty to society, to the whole.
"Chaotic" characters are all about the individual. Personal freedom and the ability to choose one's own path (rather than fit into the mold society as a whole wants/needs for you to fill) is of utmost importance. This is why chaotic characters often break the rules. The rights of the individual are greater than the rights of the whole for chaotic characters.
This dichotomy is why paladins must be lawful. They are duty bound to serve society as a whole. Paladins place the needs of the whole over their individual needs. It's also why paladins tend to have short life spans. ;-)
Caveat: Layonara is not traditional DnD, and as such, some interpretations of alignment may differ. Consult with your GM during a quest to be sure of interpretation. I simply offered this note because I find that knowing the development of an idea and where the idea came from helps us to understand the idea (in this case, alignments) much better.