Throughout our popular history of sprawling Los Angeles or, if you prefer, the more derogatory “Tinseltown” said acronym LAX may not have once enjoyed the relative frequency it does yet today: i.e. sometime before air travel here in USA could ever seem as commonplace, although certain regard must likewise rest upon the intermediate stages of technology & modernization on America’s west coast that long ago. In this respect alone, therefore, idiomatic “Los Angeles (or simply downtown) express” rather alluded to the overtaxed busline which readily supplied a constant influx of diverse artists & budding talent to our booming, motion picture industry in those gullible years then preceding WWII 1941-45. As far as I can adequately tell, moreover, the central airport to LA’s vast metropolis has no “x” in its official nomenclature—so I logically conclude this acromym in question derives from West Coast “pop” culture, rather like world-famous “Hollywood” does also from the older & more complete hillside montre of “Hollywoodland” and not really from the city’s urban district called West Hollywood (on your road map) which did in all probability give its well-known moniker to those “singing hills” that later became synonymous with our American, motion picture industry.
