Make the lavender syrup: Combine sugar and 1 cup water in a small saucepan over medium heat. Stir until sugar dissolves completely, about 3-5 minutes.
Infuse the syrup: Add dried lavender buds to the syrup. Remove from heat, cover, and let steep for 30 minutes.
Strain the mixture: Pour the lavender syrup through a fine mesh strainer into a large pitcher, pressing on the buds to extract all the flavor. Discard used lavender buds.
Add lemon juice: Squeeze lemons and add 1 cup of fresh juice to the pitcher with the lavender syrup.
Dilute with water: Add 4 cups of cold water to the pitcher and stir well to combine all ingredients.
Chill the mocktail: Refrigerate for at least 1 hour before serving for best flavor.
Serve: Pour over ice in tall glasses. Garnish with fresh lavender sprigs and lemon slices.