Combine sugar, 1 cup water, and lavender in a small saucepan over medium heat. Stir until the sugar dissolves, about 2 minutes. Remove from heat, steep 15 minutes, then strain and cool.

Blend the blueberries with the 1/2 cup water until smooth, about 30 seconds. Strain the puree into a large pitcher, pressing out all the juice. Discard the solids.

Pour the cooled syrup, lemon juice, and 3 cups cold water into the pitcher. Stir well. Serve over ice, garnished with blueberries and a lemon slice.