Grate the zest from the lemons using a Microplane grater, taking care to leave the pith behind. Place the zest in a 3-quart pitcher. Pour the vodka over it and stir. Cover with plastic wrap and set in a spot where it won't be disturbed, at room temperature, and let steep 1 week.
Combine 3 1/2 cups water and the sugar in a large saucepan and cook over medium heat until the sugar dissolves, stirring occasionally, about 10 minutes.
Let cool completely, then pour the syrup into the pitcher with the zest and stir. Cover tightly again and let stand for 24 hours. Strain through a fine-mesh sieve and discard the solids. Pour into clean bottles with tight-fitting caps. Refrigerate until well chilled, at least 4 hours or up to 1 month.