I can't think of any lawn type grass other than well, lawn grass. I
don't know in what part of the counry you're in, but I'd get a piece of
zoysia sod from the garden center and be done with it. Here in the
South, zoysia is really the best type of grass for sun and shade and
makes a very beautiful carpet.

There are several spreading ground-cover types of Sedum that I could
also recommend for filling in an area. Sedum tetractinum and Sedum
sexangulare are good spreading types that I've had good luck with.
They wouldn't be good for foot traffic, though.

There are also several herbs that can be grown as groundcover and can
stand foot traffic. Some of them would probably look grassy like the
thymes.

Is this an area that you would want to mow? Will it be walked on?
Etc...