Quick answer: The calendar month matters less than your grass type's growth cycle. Warm-season grasses (Bermuda, Zoysia, Centipede, St. Augustine) do most of their feeding, mowing, and aeration from late spring through summer, then go dormant for winter. Tall Fescue, the Piedmont's one real cool-season grass, does its most important work in fall (aeration and overseeding) and needs the most help getting through summer heat. Get the season right for your specific grass, not just the season on the calendar.
Why "what month is it" isn't the whole answer
A lot of generic lawn care advice gives one calendar for the whole country. In the Piedmont's transition zone, the more useful question is which growth cycle your grass is in right now. Warm-season grasses and Tall Fescue are doing opposite things for most of the year: when Bermuda is greening up and hungry, Fescue is heading into its hardest stretch, and vice versa. Start with your grass type on the grass type guide if you're not sure which camp you're in, then use the season pages below for what actually needs doing right now.