Who did the soil test?
IMO you don't need the lime, and should concentrate on building organic matter. I've seen too many university and ag extension tests that recommend too much lime for the pH. 6.3 to 6.7 is optimal. The gypsum will bring up your calcium and sulfur levels without affecting pH. It's a new lawn with low organic matter so be patient and give it some time.
Corn gluten next spring at 20-25lbs per thousand.