First off, alignment is relevant. Think of it as an exceptionally broad standard from which players have their character deviate. You can have that Neutral Evil character donate gifts to the orphanage, or the Lawful Neutral break a rule or two. But it's the quality of being an exception that gives such acts meaning. If the deviations become standard, however, your character is now operating within a different set of operating parameters.
By and large, I agree with Light Phoenix's description of LN, but it's one type of LN. There are others, of course, as I'm sure s/he would agree. (You'll note though that my language above indicates my belief that a predisposition towards mathematics and logic would be apt. Of course, ability with mathematics also tends to be paired with ability in music...) I have some other ideas that might add to, supplement, or complicate his depiction.
First, I would argue that anyone who describes a lawful character as having a personal code of anything is describing the operating parameters of a chaotic character. Lawfuls subsume their identity within a larger whole. They're the characters who would say, "My country, right or wrong." A modern analogy might be to think of true lawfuls as strict constructionists of the US constitution, a rule utilitarian or someone who regards the Bible as an instruction manual. (Lord, forgive me...) Basically, the idea is that you, the individual, do not have the knowledge or the ability to see the broad picture for what is best for society. So you follow a set of rules handed down by a trusted authority figure who does. This enormously simplifies your life. You don't have to figure out what the right law is; you have to figure out the intention of the Founding Fathers or Church hierarchy.
A true lawful might even find the notion of individual rights to be a foreign concept. A true lawful might see nothing wrong with charming or compelling someone after persuasion failed.
A true lawful might conceive of EVERYTHING as a contract. The PCs are bound by an implicit social contract. Promise to do something? A binding oral contract. A true lawful might do everything he says and exactly that and nothing more. A true lawful might feel that if the other party read something into his words, that was the other party's mistake, which he cannot be held accountable for. And if the other party fails to ask the right questions... well, it's only your lawful responsibility to provide the absolutely correct answers. Shade it to good or shade it to evil, these true lawfuls are the debaters and lawyers and lawyers of the party. A true lawful will always cite precedent.
A true lawful would likely be keenly aware of the relationships between party members and how they change. To him, the world might be essentially a web of relationships binding people together in various configurations. Some are more efficient than others and the closer people are bound together the better. His primary method of getting to know someone might be best described as a process of decoding them, finding out how they work, what their strengths/weaknesses are, their pressure tolerances, etc.
A true lawful could be completely amoral. He might not give a hoot about the fact that the demonic BBEG wants to make everyone evil. The fact that BBEG wants to end the world, would bother him greatly. (Demons are anarchists, you see.) True lawfuls could be the consummate nationalists, which might be the primary reason he's against the end of the world. From there, a persuasive party member might convince a true lawful of a great many things. The druid might convince him to become environmentalist because she persuaded him that to love your nation requires loving your land as well as its people. A true lawful might be perfectly willing to forcibly convert someone to the cause. He might also willing to commit random acts of kindness, because to him, they aren't random. It's an efficient use of resources to provide carrots as well as sticks.
A true lawful could have an incapacitating fear of oozes and filth, as they are the embodiment of chaos.
A true lawful might even have a hierarchy of principles to resolve conflicts efficiently. As a player, figure out what organization defines him and a few basic and unalterable rules of behavior. Violate them rarely and only for dramatic effect.
If ending slavery is the end that justifies the means, figure out what means are always already a part of the ends. If ending slavery is the goal, what authority told this character that it was a justifiable one? A True lawful doesn't end slavery because he believes that slavery is wrong or because it corrupts both its victims and its masters. True lawfuls would fight slavery because an appropriate authority told them to, because slavers had disrupted the natural order of society, or because slavery harmed the (national, clerical, business) institution the true lawful was a part of.
Is this type of character nice? No. Is he a good party member? Yes. He has his priorities straight.
roguerouge