Using a Y-shaped peeler, remove peel from lemons in 1/2-inch strips; cut peels into thin strips (about 3 cups).
Stir together lemon peel strips, vodka, and syrup in a large jar; shake to combine. Seal tightly, and place in a cool, dry place until vodka is infused with lemon flavor, about 1 week.
Pour vodka through a fine mesh strainer into a large bowl, discarding solids. Store limoncello in an airtight container in the refrigerator for up to 1 year.
