Apparently LJ gives you a quick way to build a set of RSS feeds for your journal:
http://www.livejournal.com/support/faqbrowse.bml?faqid=149 - see the OPML entry.
You'll need to hack in a quick ?auth=digest to the end of each of the RSS entries in order to make sure you get the friends-only stuff. Note that your RSS reader would have to cache these.
The major failing of LJ RSS feeds is that it still doesn't support showing comments. You'll have to click-through for those.