In a saucepan, combine water and sugar. Heat over medium heat, stirring until sugar is dissolved. Remove from heat and let cool.

In a mixing bowl, combine the cooled syrup, fresh lemon juice, and lemon zest. Stir well to combine.

Refrigerate the mixture for at least 2 hours until well chilled.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Transfer the sorbet to a freezer-safe container and freeze for at least 2 hours to firm up.