Using a vegetable peeler, remove thin layer of peel from lemons, leaving white pith intact. Reserve peeled lemons for another use.
Bring sugar, salt, and 4 cups water to a boil in a medium saucepan over medium-high heat, whisking occasionally. Remove syrup from heat, and stir in lemon peels and mint. Cover and let stand 30 minutes. Pour mixture through a wire-mesh strainer into a container; discard solids. Refrigerate up to 2 weeks.