I had a similar problem at LAX when I went on my MHD in April. I looked around for the ANA Fuji Lounge (as listed in the Elite guide); when I found it I was told that it is only used by ANA at a particular time of day - when there is an ANA flight. At the time I asked it was being used for an LH flight.

It seems that many of the lounges are not dedicated to a particular airline, but instead are used for specific flights.

I did end up getting in to a Singapore Airlines lounge, but I got the big song and dance about "you must have a Singapore Airlines boarding card". This, despite the big Star Alliance Gold sign outside the door.

They really need to get a dedicated *A lounge at Tom Bradley.