There had been a lot of talk about what to put in the run on this gardening thread:
https://www.backyardchickens.com/threads/chicken-poop.1218348/
The grass will not survive the chickens without major effort on your part. We have used leaf litter and straw, but you need a huge amount of material to keep the run from becoming a stinky, muddy mess. Can you find coir locally? I bet that would work.
We're going to fill ours with wood chips this coming season, then double down on leaf collection next fall. We'll also plant ground cover, bushes, and shrubs, then put up some strategic barriers to keep the girls from killing everything