Re
Dragonblade, yes it does. Lawful means law-abiding. Otherwise you would choose a chaotic or neutral good alignment.
Ever read about the Theocracy of the Pale in Greyhawk? A lawful neutral fantasy society. There laws are absolute and their people are expected to follow them.
Ever wonder why in D and D, every fantasy world who has a Lawful Good God of Justice. Lawful means law abiding.
What you described in the following is a Chaotic or Neutral Good person, not lawful good:
The paladin does what is good and right according to a code that your or other secular authorities may not care for, and in fact may be "illegal". But the paladin is not beholden to secular law or authority. Only to the divine law of his god while in pursuit of good.
You seem to assume that paladins are like police officers who must accord evil doers and monsters their "civil rights". They are not. They don't have to bring criminals to the "proper authorities". After all the paladin is the only true proper authority when it comes to executing the divine will of their god. And if the paladins code accords no rights to evil doers or monsters than they have none. In fact the notion of civil rights is curious one arising from the ancient Greeks and appearing on and off throughout history.
Paladins are expected to follow the laws of the land and only oppose them if they are deemed as unjust, and not necessarily good, though they cannot be evil. For example, in the FR, slavery is legal in Calimshan, yet Tyr is worshipped prominently. For most good people, slavery is wrong. Lawful Good Paladins would have to accept laws that allowed slavery to exist as long as the slaves were treated justly by their masters.
Would a Chaotic or Neutral good person have to abide such laws? Probably not. That is the big difference between chaotic and neutral good players, they aren't inclined to be law abiding. They see something wrong, they don't have to worry about legal procedure.
The very fact that you don't believe lawful is self-evident indicates that you have little concept of what lawful means. It very much does mean law abiding.
If you want to argue that what one person considers a just law when compared to another, that is open ended. A lawful person will follow the laws put in place though irregardless of the society, unless he or she is at war with the other society and cares little for respected their laws. A lawful person believes society will crumble without laws and order, and believes the following of laws and use of procedure to carry out those laws is necessary for an orderly society.
The only time a Paladin will break the law is when he or she is fighting an unjust or obviously evil law. Then they are well within their rights. They will not mete out justice in a lawless and disorderly manner. There lawful code is their lawful code whereever they may travel. They will generally follow the laws of any land they are in as long as those laws are just. If the land is lawless, then they will default to their own divine doctrine's laws or their secular cultural laws.
To Sum it up, Lawful does mean law-abiding. I think that is self-evident because of the differing descriptions in the PHB for Lawful, Chaotic and Neutral Good.