LiveJournal's HTML cleaner uses a parser which can parse HTML (but also understands XHTML).
This means, for example, that you can leave off quotes on attribute values if they consist only of letters, numbers, hyphens, dots, underscores, and colons. This is the reason why <lj user=exampleusername> and <lj user="exampleusername"> both work to produce exampleusername (though I'd prefer the latter)—the HTML cleaner doesn't see whether there are quotes or not and the output of the parser is the same in either case.
The fact that the cleaner uses an HTML parser also means that it does SGML-style attribute minimisation; if the value of an attribute in an HTML file is the same as its name, then you can leave off the value. For example, you can pre-check a checkbox in HTML with <input type=checkbox name=foo value=27 checked>, which would have to be <input type="checkbox" name="foo" value="27" checked="checked" /> in XHTML (which does not allow attribute minimisation).
And because the parser in the HTML cleaner does this, too, you can say <lj-cut text> (see it in action here: [this is cut]) and it'll be parsed the same as <lj-cut text="text"> :p Or even <lj user> which becomes user (i.e. <lj user="user">). Funny.