This FAQ mentions linking to another journal in a journal entry using a normal HTML link, but does not mention the existence of the <lj user> tag.
Here is the FAQ (my proposed changes in bold):
There are two ways to link to another user's journal from a journal entry, with an HTML tag and with a LiveJournal-specific tag (which will only work on LiveJournal). To learn how to link to another journal with a LiveJournal specific tag, please see http://www.livejournal.com/support/faqbrowse.bml?faqid=75
Here's an example of an HTML tag for a link to another journal:
<a href="http://www.livejournal.com/users/frank">Keep up with Frank!</a>
The opening tag contains the URL of the journal, next follows the text you want to appear as the link, and then just add the closing tag.
The same tags are used to link to a website:
<a href="http://www.livejournal.com/">Check out LiveJournal!</a>
I'm not sure my wording is best, it just seems like there should be some mention of the relevant LJ-specific tag in there.