In a small saucepot, add about 1 1/2 cups cold water or enough to cover the lemon peels. Add the lemon peels and bring the water to a boil over medium-high heat. Remove from the heat, strain out the lemon peels. Return the lemon peels to the pot and add in another 1 1/2 cups cold water and bring to a boil again. Repeat this process one more time.
Put the lemon peels, granulated sugar and 1 1/2 cups water into a saucepot. Bring the water to a boil until all the sugar is dissolved. Lower the heat and simmer until the lemon peels are translucent, about 7 to 10 minutes. Strain out the lemon peels and set aside until needed in recipe.