The California Desert is a large portion of an even larger desert Eco System that stretches all the way up to Eastern Oregon, across the American states of Nevada and Utah up to the Rocky Mountains, and then includes Arizona, New Mexico and West Texas, as well as North and Central Mexico.
Linguists have hypothesized that the dominant language family in the larger American Desert scene, Uto-Aztecan, had a northern and southern branch, and that the northern branch probably came from the Death Valley area of California, that the southern branch came from Mexico, and that the language itself came from today's Arizona. It's also well accepted that there were complex civilizations in this desert area as early as 500 A.D. What scholars don't know is what language the people in those civilizations spoke. They do know that these civilizations collapsed around 1200-1300 AD and that people generally moved south, from Utah and Nevada to Arizona and New Mexico, and from Az/NM into Mexico proper. This movement is echoed in the origin myths of the Aztecs, who claimed that they had "come from the North."
Although no one knows for sure what "happened" to these lost civilizations of the Western American Desert, it doesn't take a lot of imagination to point at climate change as a culprit. But looking at the ruins as well as the successor cultures, it seems fair to say that this North American civilization of the European Middle Ages- likely developed by Northern branch speaking Uto-Aztecans and incorporating other pre-existing linguistic groups and groups that migrated towards the larger settlements- belongs among the ranks of "known" World Civilizations.
You could say that they "barely" qualify on the basis of simply having some kind of water sharing arrangement and an organized religion of some sort, but based on my experience in this landscape, their achievement was damn impressive.
I think you can almost make an argument that even today this period is a "lost" civilization, and requires further inquiry.