Q.What “grass” can replace water thirsty lawns?
Someone recommended “nut grass” weed.
I would not recommend Nutsedges as a lawn alternative.
I would suggest contacting your County Extension office and talk to them about lawn alternatives specific to your area.
I have included a link to help you find your closest office.
Also some articles that offer some alternative drought tolerant lawn species.
https://www.gardeningknowhow.com/special/xeriscape/drought-tolerant-lawn-grass.htm
http://www.clemson.edu/extension/hgic/pests/weeds/hgic2312.html
https://www.gardeningknowhow.com/plant-problems/weeds/controlling-sedge-weeds.htm
https://www.gardeningknowhow.com/plant-problems/weeds/controlling-sedge-weeds.htm
http://ucanr.edu/sites/scmg/Lawn_Replacement/Water-Wise_Lawn_Alternatives/