Combine the sugar and water in a small saucepan and warm over medium heat, stirring, until the sugar fully dissolves and the liquid looks clear, about 3 minutes.

Remove the syrup from the heat and let it cool to room temperature, about 20 minutes.

Stir the lemon juice into the cooled syrup.

Pour the lemon syrup into a 3-quart glass beverage dispenser.

Just before serving, top the dispenser with the cold sparkling water and stir once gently with a long spoon so you do not knock out the bubbles.

Float the lemon slices and mint sprigs on top.

Fill glasses with ice first, then pour the lemonade over so it stays fizzy longer.