The only grasses I know of that tolerate shade are Chasmanthium latifolium (Northern Oat Grass) and Calamagrostis brachytrica. Hakoneckloas take shade, but need plenty of moisture. I would try the following plants (none of them grasses): Lamiums, Lamiastrum 'Herman's Pride', Epimediums, Saruma henryi, Liriope.

Look into Sesleria and Luzula. They'll take shade, but do require at least some water. Festuca can deal with a little shade, and is very drought tolerant once established. Same with Pennisetum orientale.

I have Lamium there It looks good in early summer but the patch has never grown big. I mean, I water during summer but moisture just disappears unlike other parts of the garden where it shows it's been watered. Thank you for your suggestions. Liliana