You mean how long will it take them to stop killing it? Forever. Chickens will tear up a lawn whether they are 4 months old or 4 years old, whether it has been there for 1 year or 10. Back when we got chickens the first time, the 6 of them took 6 months to turn a brand new 20x50 lawn into a large patch of dirt.
We have coastal grass in a 1300sq feet area, 21 birds total (lost one) and they havent managed to destory any of it. Matter a fact it seems to like the chickens poop alittle much it has spread like wild fire my yard has no more bald spots and normally by now its completely dead thanks to the weather but it hasnt died either.