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From a post in the lj_dev community on LiveJournal (http://www.livejournal.com/community/lj_dev/627644.html):
http://www.livejournal.com/users/USER/data/rss?auth=digest
Get RSS feeds (including protected entries) by authenticating with HTTP Digest Auth. Good for aggregators.
RSS Bandit supports Digest auth, and also displays the feed with a lock icon. This is good, because I can (possibly) put Bandit and my feed list on a USB thumb drive and then carry that around, without having to worry about authenticating using cookies and other things.
Of course, I should mention that this only works if you already have a LiveJournal account.