In a medium saucepan, combine 2 cups lemon juice and the sugar. Bring to a boil, stirring, until sugar dissolves. Remove from heat, and let syrup cool.
In a pitcher, stir together lemon syrup, remaining 2 cups lemon juice, and 3 1/2 cups water. To serve, pour over ice, and garnish with lemon peel, if desired.
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