What type of grass? Is it cool season or warm season. Virginians tend to favor cool season, but there are those who favor warm season. If you drive through the neighborhood, there are the folks with the brown lawns after the temperatures drop.
If you are ever in doubt about any gardening issue, the local Cooperative Extension Services in VA are the best I ever encountered. They confirmed my love for horticulture. You can find your local Cooperative Extension Service Agent's telephone number in the phone book. They usually offer many irresistable gardening and landscaping classes.
Soil testing is very important to determine what your soil needs. Does it need fertilizer? What does your soil test reveal? Do you need to add additional nitrogen. Lawns too rich in nitrogen tend to be subject to disease. Most VA lawns need lime.
If you are overseeding, you are somewhat getting a late start. The latest seasonal application of fertilizer is usually recommended the 1st 2 wks of September. Lawn renovation should have begun before now. Then, you need to get the grass germinated, growing, and mowing before adding the fertilizer. But, why would you add amendments without knowing for what the soil needs.
Get a soil test. Your local Cooperative Extension Agent can help you with this, provide you with an annual lawn maintenance program, and provide opportunities for education about landscape management.