In a large pitcher or heatproof bowl, combine 1 cup granulated sugar and 1 cup hot water, stirring until the sugar is completely dissolved.
Set the simple syrup aside to cool while preparing the lemons.
Roll the lemons on the counter, cut them in half, and squeeze until you have 1 cup of fresh lemon juice, discarding any seeds.
Pour the fresh lemon juice into the pitcher with the cooled simple syrup.
Add 3.5 cups cold water (start with 3 cups, taste, then add the remaining 0.5 cup if desired for a milder flavor) and stir well to combine.
Refrigerate the lemonade for at least 60 minutes to chill and allow flavors to meld.
When ready to serve, fill glasses with ice and pour in the chilled lemonade.
Garnish each glass with a fresh lemon slice and a sprig of mint (optional).