This hits it on the head for me.
Lawfuls are organized and if a character is lawful, will always gravitate towards longer term thinking, orderly conduct, and is probably most comfortable in a hierarchical structure. They see the group as a more important entity and the individual should be responsible for and to the group.
This is why I always disliked 3e's take on demons and devils. You had demons like Malcanthet that were organized, long term planners with plots within plots. That's the opposite of chaotic to me. Chaotic is impulsive. That's, to me, the basic difference between a lawful and a chaotic character. A lawful character will sit down and try to come up with a plan, whereas the chaotic character dives right in feet first.