The Central Valley has never been a fully arid desert as long as there were not farmers there diverting the water. When they created a desert (in the 1800s), the federal government stepped in and diverted water from even further north and east. Of course, the farmers didn't do it all on their own, as lakes were drying up in California before they got here.
This isn't true. There is a natural rain shadow in the southern San Joaquin Valley.
The California Aqueduct takes water from the Sierras and Central Valley and supplies southern cities like San Luis Obispo, Santa Barbara, LA and Palmdale.
I'm not really sure what you're referring to by "the government stepped in and diverted water" comment. Or by "all the lakes were drying up before they got here".
While the southern San Joaquin Valley does indeed get very little rainfall, the mountains that drain in to it normally get plenty of water.
Tulare Lake, once the largest body of fresh water west of the Mississippi, was right in the middle of the driest parts of Kern and Tulare counties.
The lake has even reappeared following a period of unusually high precipitation and as recent as 1997.