Place the lemon peels in a 2-quart pitcher. Pour the vodka over the peels and cover with plastic wrap. Steep the lemon peels in the vodka for 4 days at room temperature.

Stir the water and sugar in a large saucepan over medium heat until the sugar dissolves, about 5 minutes. Cool completely.

Pour the sugar syrup over the vodka mixture. Cover and let stand at room temperature overnight.

Strain the limoncello through a mesh strainer. Discard the peels. Transfer the limoncello to bottles. Seal the bottles and refrigerate until cold, at least 4 hours and up to 1 month.