Hull and slice the strawberries, discarding bruised areas
Combine sugar and water in a saucepan; cook over medium heat until sugar dissolves
Blend strawberries until smooth in a food processor
Add cooled simple syrup, lemon juice, and zest to the puree; stir to combine
Chill the mixture for 2 hours in the refrigerator
Churn in an ice cream maker according to manufacturer instructions
Transfer to a freezer-safe container and freeze for 4 hours, or until firm