Cut lemons into slices about 1/4 inch thick and remove the fruit pulp. Cut the rings in half so the peels are in long strips.
Bring water and lemon peel to a boil in a small pan. Drain water, and repeat with fresh cold water. Repeat the boiling step three times (see Editor's Note). Drain and set peels aside.
Combine 2 cups fresh water with 2 cups sugar. Bring to a boil, stirring to dissolve the sugar. Reduce heat to low and stir in citrus peels; simmer until the white pith is translucent. Store peels in syrup, refrigerated, to keep them soft, or allow them to dry. Toss dry candied peels in additional sugar and store airtight at room temperature.