Bring water and sugar to a boil in a small saucepan, stirring occasionally, until sugar dissolves. Let cool.
Mix sugar syrup and lemon juice in a nonreactive 9-by-13-inch baking dish. Cover, and freeze overnight. (Lemonade can be frozen for up to 3 days.)
Using a fork, break frozen lemonade mixture into chunks, and transfer to a large bowl. Whisk, breaking up chunks, until slushy. Divide slush among glasses. Squeeze 1 lemon wedge over each glass, drop it into glass, and serve immediately.
The lemonade mixture can be made and frozen up to a week in advance.