Remove the zest from the lemons in wide strips with a vegetable peeler, taking only the yellow part and carefully avoiding even the slightest bit of underlying white pith, which would turn the limoncello bitter. Reserve the zested lemons for another use.
Pour the alcohol into a clean quart (1-liter) jar with a tight-fitting lid, such as a European-style canning jar with a rubber gasket and clamp lid. Add the lemon zest, close the jar, and let it steep in a cool, dark place, such as a pantry or cellar, for 1 week.
After the alcohol has steeped for 1 week, stir the sugar and water together in a large saucepan over low heat until the sugar dissolves completely. The mixture should be clear. Remove from the heat and let cool completely. (Do not be tempted to rush into the next step; if the sugar syrup is not completely cool, your limoncello will be cloudy.)
Remove the lemon zest from the alcohol and discard. Pour the infused alcohol into the sugar syrup and stir to combine. Pour the mixture through a fine-mesh strainer lined with cheesecloth, then decant the limoncello into clean bottles and seal with a cork or lid of some sort.
Let the limoncello mature for 15 days in a cool, dark place, then refrigerate. Serve chilled.