Place mint leaves and lime juice in a cocktail shaker and muddle well.
Pour rum and lavender simple syrup into the shaker. Fill with ice and shake well. Pour into a glass.
Top with club soda.
Notes
If you want a lavender color you can squeeze frozen blueberries or add purple potato powder into the glass until you have the desired color. I tried both and they both worked well. In the photos above I used frozen blueberries.Taste after 1 ounce to see how you like it. You can always add more rum, but you can't take it away.