In a saucepan, bring lime juice, sugar, lime zest, and 2 cups of water to a simmer over medium heat. Stir until the sugar is dissolved, about 6 minutes. Remove from heat, add the mint leaves to the pot, and set aside at room temperature for 30 minutes. Strain through a sieve into a 1 quart pitcher. Add the cucumber slices and place in the fridge to chill. Just before serving, pour the liter of sparkling water into the pitcher, and serve over ice.