Reserve 1 lemon for garnish. Remove wide strips of zest from 2 lemons with a vegetable peeler (do not remove the pith). Juice enough of the lemons to make 2 cups lemon juice.
Add the lemon zest strips, sugar and 1 1/2 cups water to a medium saucepan and bring to a boil, stirring until the sugar is dissolved. Turn off the heat and stir in 1/2 teaspoon salt. Discard the zest strips and let cool for 15 minutes.
Pour the simple syrup into a pitcher and stir in the lemon juice and 2 cups cold water. Divide the mixture among three 12-compartment ice cube trays and freeze until solid, 8 hours and up to overnight. (The ice cubes will not be as solid as ice.)
Add the lemonade cubes and 1/2 cup cold water to a blender and blend, stopping the blender and stirring as needed, until the mixture is smooth and pourable. Pour the lemonade slushie into four 8-ounce glasses. Slice 4 thin slices from the reserved lemon and garnish each glass with a lemon slice.
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