For the lemon mint syrup, combine all ingredients except the mint in a medium pot. Cook over medium heat, stirring occasionally, until simmering. Continue to simmer for 2 minutes and remove from heat. Add the mint leaves and allow them to steep in the pot as the syrup cools to room temperature.
Strain the syrup and refrigerate in a sealed container until ready to use.
In a large pitcher, muddle the mint leaves, cucumber slices, and syrup. Add the lemon juice and gin, stir well. At this point, you can put the pitcher in the fridge to keep until ready to serve.
Just before serving, add the sparkling water to the pitcher and stir. Fill 8 glasses with ice, divide lemonade among glasses and garnish with mint.