Here is second image.

Sketch of what I was thinking. Thanks!

The trouble with your pictures is that they look unrelated. There's no way to tell how the 2nd picture fits with the first. And the plan doesn't help because the arbor business does not show up there either.

Guessing, I'd think you'd want the grass shape almost opposite of what you're proposing. I'm thinking it would look better if the grass were fatter at its central area -- like oval or similar -- rather than pinch-waisted. Is the line of squares, stepping stones? Why duplicate a path that the grass could serve just as well?

You'd be doing yourself a favor if you make any edging flush with grade and at least 8" wide. The usually stuff people do detracts rather than adds.

Are you flipping this house, and therefore looking for something attractive and quick? Or is this a 'keeper', where you are constrained by budget but can invest the time?

I agree, the photos aren't in relation to one another. I have no idea what area the second photo is showing, or what direction it's facing.

Basic questions:
1) This being CA and a drought situation, what's your water requirements?
2) What's your Sunset zone, which is much more useful than the USDA zone?
3) How much sun, and how many hours of the day?
4) What is the expected usage of this space? Decorative? A BBQ grill and seating somewhere? A place for kids to play?

If you want free advice, specifics are essential.

I see pavers under the pergola, so I assume the paver area in your sketch is where the pergola is. That's a nice pergola and if you clean up all the junk, it could be beautiful with a nice table and chairs. You could hang lanterns for lighting, and even put a fire pit in there for cool evenings.

I agree that a more oval lawn would look nice.

Please answer the basic questions in the post above. It will help us help you.