Add peels to a medium saucepan, cover with water and bring to a boil. Drain. Repeat 4 times. This step is important to remove the bitterness. Cool.
Cut lemon peel in julienne strips about ¼” wide.
In a medium saucepan add 2 cups of water and 2 cups of sugar, stirring to dissolve sugar. Reduce to low. Carefully add julienne lemon strips and simmer gently until all the white pitch is transparent, about 30-45 minutes.
Store peels in cooled syrup or allow them to cool and roll them in sugar. Store in an airtight container.