How to Make It
Combine all of the ingredients in a medium saucepan and bring to a boil. Cook over moderate heat, stirring, until the sugar dissolves, about 3 minutes. Remove from the heat, cover and let steep for 2 hours. Strain the syrup through a fine sieve.
In a mini food processor, pulse the basil with the lemon juice until minced. Scrape into a large pitcher. Stir in 11 ounces of the lavender syrup (any remaining syrup can be refrigerated for 2 weeks) and the grapefruit juice, the bitters and sparkling water. Strain into ice-filled glasses and garnish with basil.
For a cocktail version, use 24 ounces sparkling water plus 16 ounces gin or vodka.