Hello,

You probably want to plant Highland or Colonial bentgrass.  There are about 6 million seeds per pound and the seeding rate is 1 lb. per 1,000 sq. ft.

You can find it online.  I found one source here:

https://www.outsidepride.com/seed/grass-seed/bent-grass-seed/highland-colonial-bent-grass.html?gclid=CjwKCAiAp8iMBhAqEiwAJb94z-b6uyJzW4Rhu_BqTR64f0hDTABbAx0nqdrOVaR03wcfUp9GKpNGLRoC-LsQAvD_BwE

5 lbs. costs $35.00.

The other option is fine fescue (creeping red).  But this species may not blend as well with your existing lawn.  My guess is that your existing lawn is bentgrass.  If you send some photos, I may be able to tell you what grass you have.  Send a photo from about 20 feet looking over a large part of your lawn.  And send a close up photo with your elbows on your knees looking straight down.

The seeding rate for fine fescue is 6 - 8 lbs. per 1,000 sq. ft.  

Plant in the spring between April 15th and April 30th.  This will give enough time to get established before the drought comes.  I would also water it some the first summer just to get it through some of the really hot days.  After the first summer, it should be fine on its own.

Also, keep in mind that even bentgrass can die during the summer if the drought goes too long.  For example, if there is a dry spring or an extended summer.  

I hope this helps.