See all the reasons why: https://bobscaping.com/september-is-lawn-month/
There are two seasons of the year in the midwest and northeastern United States (and similar climate zones) when your odds of lawn seeding success greatly improve: Spring and Fall. Spring is second best.
Fall is also the best for killing weeds, since they are still actively growing and storing energy reserves for winter. Of course you shouldn’t seed and attempt to control weeds at the same time. Those procedures should be separated by 4 to 6 weeks.
This time of year is also excellent for testing your lawn soil (video: https://youtu.be/B51dgpJF8vs) and correcting any deficiencies, typically with lime and basic nutrient applications. Some nutrients may actually be “locked up” by having the wrong soil pH. You can learn more about that here: https://bobscaping.com/soil-ph/
While I would put getting your soil pH and basic nutrient levels correct as priority #1, there is one thing you should do to your lawn at least once a year: CORE AERATION (photo above). For the best results, soil shouldn’t be too wet or dry. Seeding thin spots in your lawn is a great follow-up to core aeration, since seed will grow quite well out of those aeration holes. Leave the soil cores on the lawn to breakdown on their own.
More on lawn aeration here: https://bobscaping.com/lawn-aeration/
This Bobscaping video will provide some useful tips: