Combine the granulated sugar and 0.5 cup water in a small saucepan over medium heat, stirring until the sugar dissolves, 2–3 minutes. Remove from heat and let cool to room temperature, about 10 minutes.
Add the cubed watermelon to a blender and blend until completely smooth, 30–60 seconds. Strain the puree through a fine-mesh sieve into a large bowl or pitcher, pressing to extract as much juice as possible; discard the pulp.
Juice the lemons to yield 1 cup of fresh lemon juice, then strain out seeds and excess pulp.
In a large pitcher, combine the watermelon juice, lemon juice, cooled simple syrup, and 1 cup cold water. Stir until evenly mixed and bright pink.
Fill glasses with ice. Pour the watermelon lemonade over the ice and garnish with mint leaves. Serve immediately.