In a small saucepan, combine the water, granulated sugar, and chopped mint leaves. Heat the mixture over medium heat, stirring continuously until the sugar has completely dissolved and the mixture comes to a boil.
Remove the saucepan from the heat and allow the mint syrup to cool for about 1 hour. Once cooled, strain the syrup to remove the mint leaves.
Fill two cups or chilled goblets with crushed ice. Pour half of the lemonade into each cup.
Drizzle the mint syrup over the lemonade and ice, dividing it evenly between the two cups.
Garnish each cup with a sprig of fresh mint and add a straw. Serve immediately and enjoy the refreshing taste of your homemade alcohol-free Mint Julep.