Wash and stem grapes. Pass grapes through a food mill, not allowing any seeds through but including all pieces of pulp on skin that come through. Refrigerator.
Make simple syrup by heating sugar and water until clear and refrigerator. When ingredients are cold, add simple syrup to grape pulp. Add lemon juice and zest and stir to mix well. Whip cream to soft peaks and fold into cold grape mixture. Place in ice cream machine and chill following machine instructions. When finished, pour into 2-ounce Dixie cups. Cover with plastic wrap and freeze. To serve, remove from freezer and allow to stand 10 minutes. Unmold into a martini glass and garnish with fresh cream and clean grapes.