Peel the skin off of the lemons with a vegetable peeler, being careful not to get any of the bitter pith. Chop the peels into the size of large sesame seeds. You should have about 2 tablespoons.
In a medium saucepan over medium-high heat, bring 1 cup water, sugar and lemon peel to a boil until the sugar is dissolved and the liquid is clear. Remove from the heat, stir in 1/2 cup water, fresh lemon juice and salt; this will help bring the temperature of the liquid down. Chill completely in the refrigerator, 2 hours.
Freeze the mixture in an ice cream freezer according to manufacturer's directions.
It is very important to the flavor that you freshly squeeze the lemon juice for this recipe; store-bought lemon juice often has an extremely metallic taste.