Welcome to Flyertalk BertramCooper, glad you found us!
I was at LAX T2 SkyClub last night. The shower rooms were definitely there, though I can't tell you if they were functional as I did not use them. The club closed at 11 'due to construction' though I observed no construction zones so they could be working on the showers for all I know.
They did give me a pass to move over to the VA lounge (just across from the SkyClub) which stayed open later. I did not notice if they had showers though.