The weed is dallisgrass. If you are in SoCal zone 10 the grass could be almost anything, because just about any grass will grow well there. Do you ever see seed heads on the grass? If you find seed heads to take picture of, the pictures of grass are better when taken in shade or under cloudy skies.

noinwi -- you are "the bomb"! That's it! Thank-you so much for the help. Now that I know the name of it, I've found lots of information on it to read. Surprisingly to me, there's more information on how to grow it, than on how to kill it. Growing it must not be too difficult, since it seems to do quite a good job in my beds on its own. Have a great weekend, and thanks again for the help. Arden

Yes, that looks like it and would make a lot of sense, so it's almost definitely that. From what I understand this should be ok considering what the owner wants. I've already offered to enhance the turf, and even though I'm paid well, he simply doesn't want to at this point. Japanese Stilt Grass sounds like it should be able to handle mowing

It could be Spurge. I can't really tell from the picture, it's too bright. If it looks like the linked weed then it's fairly easy to kill but keeping it away will be harder. It looks like the majority of the area pictured is weeds. It gets to a point where trying to save some lawn is more taxing than a complete redo. Some say the tipping point is ~50%. Aerating or doing anything to disturb your soil is going to bring up weeds seeds. Using good herbicides, Tenacity at seeding and Prodiamine thereafter can help with weeds.