It is too late to get a lawn started from seed but too early for dormant seeding…more on that HERE.
By law, I can only recommend our Winterizer/See Starter Lawn Food be applied to newly seeded lawns or lawns that test low for phosphorus…you will have to make that determination yourself. Having said that, the final feeding with the appropriate food, should be made right away so the lawn can use the food and then go dormant. Feeding later than this will stimulate the lawn right as it should be going dormant. Fresh root growth too late in the season can be killed by freezing rendering the last feeding pointless.