Bring lemon peel, sugar, and water to a boil; boil for 30 seconds. Remove from heat and add the lemon juice. Cool to room temperature and store syrup in the refrigerator. For each glass of lemonade use 1/4 cup of syrup with a cup of fizzy water or plain water. To make lemonade ice cubes, stir 2 tablespoons of syrup per cup of water and freeze as lemonade ice cubes.