Add water and sugar to a pot and bring to a boil over medium high heat, mixing until the sugar is fully mixed in. Lower heat and simmer 5 minutes. Take mixture off of heat and let cool to room temperature. Mix in lemon juice and rind.
Freeze in ice cream maker following manufactures directions until mixture is slushy. Or, spoon mixture into and 8 inch square baking dish and freeze until slushy, about 2 hours.
Spoon mixture into a bowl and beat until fluffy, then pour back into pan and freeze another 6 hours or overnight.