Remove the zest from the lemons with a vegetable peeler; combine with the vodka in a large pitcher. Cover and keep in a cool, dark place for five days. Strain and discard the zest.
Simmer the sugar and water in a large saucepan, stirring, until the sugar dissolves, 4 to 6 minutes; let cool. Stir into the vodka mixture. Refrigerate for up to 1 month.