If you are looking for a dog-friendly lawn alternative, you may be considering kurapia (lippia nodiflora). There is a new hybrid version that, according to the California Center for Urban Horticulture, is no longer considered invasive and is relatively low water. I read about it in Sunset magazine and decided to try it. We installed it about six months ago in a part of our yard that gets full sun and partial shade.
The Pro’s and Cons of Kurapia: my observations
It seems to use less water than the lawn we had.
It tolerates foot traffic moderately, only slightly better than lawn, I think.
In partial shade, it is lush and green, and forms a thick curly carpet a few inches tall that creeps beyond its borders, and it has many pretty, small, white flowers.
But, I cannot recommend Kurapia for dogs.
Where my dog plays fetch and jumps, it gets torn up just as lawn does. I do not yet know if it will grow to fill in and I dont think seeds are available to patch it up.
It seems more resistant to dog pee than lawn, but it does get damaged.
Its most damming feature, in my opinion is that is that the flowers attract many, many bees! I did not want my dog or anyone else hanging out in it. I trimmed the plants down with a weed whacker to minimize the flowers, but alas the thick curly green carpet looks pale yellow and vulnerable to foot traffic.
So, I am still waiting for a good dog friendly attractive alternative to lawn. Let me know if you find anything good for southern California: firstname.lastname@example.org