As the dark-purple carrot syrup mixes with the Champagne, this drink turns a pretty pink hue.
In a small saucepan, bring 1/2 cup water, the sugar, and carrot to a boil, stirring until the sugar dissolves. Reduce heat to low. Add the lemongrass and lavender. Let simmer until the syrup is reduced and colored by the carrot, about 30 minutes. Discard the carrot.
Fill 4 flute glasses with the Champagne. Drizzle 1 tbsp. syrup into each glass.