I don't blame the OP for his confusion ... Lounge Access has to be the single most complicated rules-question I've seen.
According to the United Web site (
http://www.united.com/page/article/0,1360,3113,00.html), *A Gold should get you into ALL of the Lufthansa lounges (except in Stuttgart (STR) and Hamburg (HAM)).
But it seems like LAX has a new category ...