First off, SA won't make the cut.
"each nation will have its own law system, judicial system.."
Pretty sure the judicial system for all states don't differ that much. And since LC is based on NY, and VC on FL, I don't think there'd be much difference since both States are from the East Coast, and both have big urban municipalities. Though, you've got a point, there are laws that only differ by State. But there will always be a higher branch of law which caps all the States in America - the federal laws, or basically, everything under the constitution.
Let's not make the work too hard for the big boys behind the scenes. It's not necessary to give LC or VC a number of their own unique State laws, in my opinion. Maybe we should just stick to the constitution and not make things more complicated, unless @Mistah Len & Co. decides it's a good thing to be added.
LC and VC having each of their own courthouse is already a problem. Nobody's opt to become a judge, yet, nor everyone else would like to cooperate in a simple trial proceeding. Most of them think it's boring, and I can't blame them.