In a small heavy saucepan dissolve the sugar in 2 1/2 cups water, without stirring, over medium heat. When the sugar is dissolved, boil for 5-6 minutes. remove from the heat and let cool.
Combine the cooled sugar syrup and lime rind and juice in a measuring cup or bowl. Stir well. Taste and adjust the flavor by adding lemon juice (for tartness) or confectioners sugar ( for sweetness). Do not over sweeten.
Freeze the mixture in a n ice cream maker, following maufaturer's instructions.
If you do not have an ince cream maker, pour the mixture into a metal or plastic freezer container and freeze until softly set, about 3 hours.
Remove from the container and chop coarsely into 3 inch pieces. Place in a food processor and process until smooth. Return to the freezer conatiner and freeze again until ser. repeat this freezing and chopping process 2 or 3 times, until a smooth consistency is obtained,.