Bring sugar, water, mint leaves, and dried lavender to a boil in a medium saucepan over medium-high heat, stirring just until sugar dissolves. Boil 2 minutes. Do not stir. Remove from heat, and press through a wire-mesh strainer into a bowl, using back of a spoon to squeeze out liquid. Discard solids. Cool completely for about 30 minutes. (This simple syrup can be stored in the refrigerator for up to 3 months).
To make the cocktail:
Place 1/2 cup of the simple syrup, ice, and lemon juice in a cocktail shaker. Shake well to combine about 45 seconds. Pour into cocktail glasses and top with a dash of club soda or sparkling water. Garnish with dried lavender stems. Enjoy with friends!