Flying to the South Pacific recently from the UK, we stopped off in LA for a few days. We had all of our dive gear and more (a bicycle). we planned to leave our luggage and fly cheaply to Phoenix.
At present there isn’t a left luggage facility in LAX.
the solution was, either upgrade to business class and for $50 we could take loads of luggage each,
or, LAX Luggage storage http://www.laxluggagestorage.com/ on (310) 670 4186 an amazing company who with one phone call, came to where i was standing in about 10minutes, took the lot for a few dollars a day each bag, and when i flew back, called up and hey presto,it arrived right outside the departure gate at the correct terminal. right where i was standing. i did not know they existed until 30seconds before i rang them. Magic.