Cut the watermelon into large pieces, discarding the rind. Place in a food processor and purée. Strain the puréed watermelon through a fine strainer to remove the pulp and seeds (this should yield about 3 cups of watermelon juice).
In a small bowl or measuring cup, combine the gelatin with 1 cup of the watermelon juice; let stand for 3 minutes. In a small saucepan, over medium heat, warm the remaining watermelon juice and the sugar until the sugar has dissolved. Whisk in the gelatin mixture and lemon juice. Remove from heat.
Lightly oil an 8-inch square glass baking dish. Pour in the mixture, cover, and refrigerate overnight. To serve, cut the jelly into cubes and divide among individual bowls. Drizzle the sparkling wine over the top, if desired.