Combine 1/2 cup water and sugar in a saucepan. Bring to a boil over high, making sure to stir until sugar dissolves. Remove from heat and add mint leaves and lavender. Allow to steep for 15 minutes. Pour through a strainer into a bowl and discard solids. Allow to cool completely.
Combine cucumber and lime juice in a food processor. Process until smooth.
Combine mint-lavender simple syrup, cucumber-lime puree, and club soda in a large pitcher. Stir well. Serve over ice and garnish with mint sprigs and lime wedges.
Add a splash of gin to turn into a delightful summer tipple.
For a lower calorie sugar substitute, try Swerve instead of granulated white sugar.