Fill a tall collins glass or other tumbler with ice.
Fill shaker with ice. Add gin, lemon juice, lavender simple syrup, and egg white. Shake for 30-45 seconds. Strain into collins glass. Top with club soda and lavender flowers for garnish, if desired.
To make lavender simple syrup:
Combine water and sugar in a small saucepan over medium heat. Stir until the sugar has dissolved. Remove from the heat and add the lavender flowers. Cover the saucepan and allow to steep for 10 minutes. Remove lavender and strain syrup into an airtight bottle or container for storage. Add a drop of violet food coloring, if desired. Chill in the refrigerator before use.