For the syrups: Put all the ingredients for each syrup into 2 separate medium saucepans and bring them to a boil over medium-high heat. Remove them from the heat; cool and strain.
For the Italian Ice: Put a large bunch of ice in a food processor and process until it is finely ground. Or put the ice in a towel and pound it with a rolling pin or bat until it is finely ground. Scoop into dishes and top with Lemon Syrup or Tutti Frutti Syrup, or both!