Bring 3 cups water and sugar just to a boil in a medium saucepan over high heat, stirring until sugar dissolves. Remove from heat. Cool.
Process sugar syrup and lemonade, in batches, in a blender until smooth. Strain and discard pulp, if desired. Stir in maraschino cherries. Cover and chill 2 hours.
Pour mixture into the freezer container of a 1-gallon ice-cream maker, and freeze according to manufacturer's instructions.