Sigh. No. Divorce Lawful from actual laws. It's easier to understand it that way. Lawful means an adherence to an external authority, and how much obedience you believe you owe to an authority. Laws are the written and enforced expression of an authority's will, so if you respect the authority those laws emerge from, you will naturally obey those laws.

Chaotic means an adherence to an internal authority (your conscience, ethics, whims, emotions, etc) over any external factor.

A bandit can be lawful even when he's breaking the law by robbing others, because he has an unswerving, faithful obedience to his leader. A member of the city watch can be chaotic, even if he's in charge of enforcing the law, because he's a wild maverick who goes off on his own to do his thing and rarely does things "by the book."

If you take a Lawful citizen from one nation and put them in another, they will analyse the alleged authority they are now under, and decide if they recognise it as an actual authority. If they do, they will obey their laws. If they don't, they will not. This is why a paladin can fight slavery in a country where slavery is legal, because a paladin would not recognise the authority of any king or emperor who legalises slavery, and therefore is under no moral or ethical compunction to obey his laws.