It's looks like I've solved problems with my iTunes account. Now, I hope, you are able to download LiveJournal.app via iTunes.
Please, let me know is everything okay or not.
P.S. It took a long time because of I have no Apple Store here in Russia to buy iPhone developer license, and need to send some faxes to Apple Support, and they parse it to slow... But, anyway, it's done and I'm happy ;)