If your client is popular enough, you've undoubtedly received emails asking for invite codes; perhaps it would be a good idea to incorporate messages into your client informing the user that if they do not have a LiveJournal, then they must get an invite code from a current user, and that the author will not give out any. A note on the downloads page might help too.
My idea: Include that message into the installation program. Since it'll obtain the actual program and the .NET runtime from the server, users who don't have an LJ account wouldn't download anything except a small (32-64k or so) EXE. If I were a user, I'd be pretty pissed if I downloaded 21 MBs and was then told I couldn't use it.