Combine 1 cup water, sugar, and fresh mint leaves in a saucepan over medium heat. Bring to a light boil, stirring occasionally, until sugar is dissolved, about 5 minutes. Remove from heat; stir in lemon zest. Let syrup cool slightly, about 10 minutes.
Mix remaining 1 1/2 cup water, lemon juice, and limoncello liqueur into syrup.
Pour mixture into an ice cream maker; churn according to the manufacturer's instructions, 10 to 15 minutes. Freeze until firm, about 6 hours.