Add the sugar, 1 cup water and lemon zest to a medium saucepan over medium heat and stir until the sugar has dissolved. Stir in the remaining 1 1/2 cups cold water, the lemon juice and limoncello. Place in the fridge until chilled, about 2 hours. Add the cold lemon mixture to an ice cream maker and run as directed by the manufacturer's instructions. You want it to look like soft serve. Remove to a plastic lidded container and place in the freezer until firm, about 3 hours.
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