Squeeze 1 cup lemon juice.
Dissolve sugar into water and lemon juice mixture. Freeze according to ice cream maker directions.
Syrup Method (for super smooth finished ice)
In a medium saucepan, combine water, sugar, and lemon zest. Stir over medium heat until sugar dissolves and mixture comes to a boil. Boil gently without stirring for 5 minutes. Place a fine strainer over a medium bowl. Pour syrup through strainer to remove lemon peel. Cool to room temperature. Stir in lemon juice. Chill in refrigerator for 30 minutes. Churn-freeze according to ice cream maker directions.
Makes about 2 quarts.