I'm another of those people that believe that using the word "Lawful" to describe one of the 4 arms of alignment was a really bad move, though an understandable one. We're all human, after all.
Anyway. Lawful means Orderly. Lawful does not mean Jurisprudence.
Order, the concept of order, does not change from place to place they same way that local laws can, such as PCs chewing gum example above. Order at its core means things doing what they're supposed to in the manner that they're supposed to and interacting in a structured, regulated manner. Thing X acts in way Y becuase that's how it's supposed to.
Lawful aligned people would interact with local legislation differently depending on the second component of their alignment. Generally speaking, of course.
A lawful good person would generally adhere to an area's laws so long as doing so in an individual instance was to the benefit of the people. Don't kill unless it's in self defense - easy. Don't steal - easy. Don't rape - easy. Don't chew bubble gum - easy, as chewing bubble gum isn't that big a deal for anybody. If a woman does not wear a hat in your presence you are required to beat her - no; because despite what they law may be, the LG person would easily recognise it as being harmful and wrong-headed. If a slave looks you in the eyes, you must have them put out - no; again, the law is not morally right and the good portion of their alignment would protest. And so forth.
A lawful neutral person would generally adhere to an area's laws so long as doing so was to the benefit of the society, rather than to the benefit of the people that make up that society.
A lawful evil person would generally adhere to an area's laws so long as doing so was to the benefit of himself. Twist the system to your advantage. Do with what you can get away with. The appearance of fairness is more important than the practice of fairness. It's not what you know, it's what you can prove.
In all, though, a Lawful person is lawful (to say, orderly) even in a vaccuum. Even in an area that has no laws that punish lying, giving false witness, or breaking a contract a lawful person would still keep their word, tell the truth on what they considdered important matters (what's important to them being in part determined by the G-N-E portion of their alignment, again), and uphold their end of a bargain. A lawful person wouldn't enter into a contract they had no intention of honoring, because once they're comitted, they're comitted. A lawful person would not make make promises they had no intention of keeping; to a lawful person a man is as good as his word. The examples could go on and on. Lawful people act how they're supposed to, because they're supposed to.
A lawful person is orderly, structured, disciplined, and conventional in their personal affairs, outlook and mannerisms. An area's legal structure has no bearing on the way in which they conduct their lives; they're Lawful no matter what local legislation may be.