In a medium saucepan over medium-high heat, combine the sugar and water. Stirring constantly, bring to a boil. Let cool 10 minutes.
Meanwhile, place the watermelon and lemon juice in the container of a blender or food processor. Process until smooth. Pour through a fine-mesh sieve into a large pitcher. Discard any solids.
Add the sugar syrup to the watermelon mixture, stirring to blend. Cover and refrigerate at least four hours. When ready to serve, stir in the carbonated water. Serve immediately over ice.