Unfortunately yes, you are held by the laws where LJ is located - it's in the TOS that you agreed to when you signed up. It's the same at Yahoo, you agree to be bound by the laws of wherever they are in California, ditto for Google and virtually all other websites, especially the big social/blog/community sites.

And then you may also be bound by the laws in your own country as well - for example, Yahoo has to follow French laws regarding Nazi artifacts for French users viewing Yahoo's site (mainly in regarding to Yahoo auctions, but all of Yahoo is affected). Germany blocked all of Compuserve at one point because they failed to follow German law even tho the data was legal in the US where Compuserve was located.

While the internet may be global, the servers providing the content are not and must follow the laws at their company's geophysical location.

Conversely, Spamhaus.org (a reputable spam blocking service) is located in the UK which has very stringent laws against frivolous lawsuits and thus is immune to lawsuits filed by spammers attempting to get the blocks on their spam removed. So sometimes having to follow local laws can be useful.