This mocktail is proof positive that alcohol-free drinks don't have to be a snooze.
In a small saucepan, bring the sugar, lemon juice, lime juice, and lavender to a simmer over medium heat, stirring until the sugar dissolves. Remove from heat. Steep for 10 minutes; strain. Let cool completely.
In a cocktail shaker, shake the lavender syrup and egg whites until foamy, about 20 times. Add ice and shake until chilled, about 10 times. Strain into 4 coupe glasses. Top with club soda. Garnish with the lemon and lime zest.