Wash and stem grapes. Pass grapes through a food mill, not allowing any seeds through but including all pieces of pulp that remain on the skin and pass through. Refrigerate.
Make simple syrup by heating sugar and water until clear. Pour simple syrup into a stainless-steel, non-reactive bowl and refrigerate until cold. When ingredients are cold, add the simple syrup to the grape pulp. Add the lemon juice and zest, and stir to mix well.
Place the mixture into an ice cream machine and chill according to the machine instructions. In a medium-sized bowl, whip the cream to soft peaks. Gently fold the whipped cream into the cold grape mixture, serve garnished with lemon zest and grapes.