Place 1/2 cup of the water and the sugar in a small pot. Set over medium-high heat and bring to a boil. Cook, stirring, until the sugar has completely dissolved and the liquid is clear, about 1 to 2 minutes. Pour this mixture into a 4-cup capacity container. Mix in the remaining 1 1/2 cups of cold water, lemon juice and pomegranate juice. Cover and store in the fridge until needed.
When ready to serve, fill 6 tall glasses each with 4 or 5 ice cubes. Pour in the lemon/pomegranate mixture, filling each glass three quarters full. Top up each glass with the sparkling wine or soda water. Serve garnished with a half lemon slice and a mint sprig.