Pretty much what everyone has said. Or you can think of it this way.
Stereotypical Lawful person in this situation: "Wow these guys' traditions are totally different from mine. Someone should tell them they are doing it wrong."
Stereotypical Chaotic person in this situation: "These guys' traditions are totally different from mine. That's pretty cool, but I'm still going to keep doing my own thing and not be influenced by them."
So a Lawful person would not necessarily follow another country's laws because they are different from the traditions and rules they believe in. Of course if the country has similar values to what he is used to, he might fit right in.
A Chaotic person would not necessarily follow another country's laws because he doesn't think traditions and rules are important anywhere. Of course if he decides he likes the way things are there, he is free to adopt their customs or combine them with his own ideals.
If a person has no bias to one extreme or the other, (or has a "When in Rome, do as the Romans do" attitude) they are probably Neutral.