Use a zester to remove the zest of the lemons, discarding the bitter white pith. Combine the lemon zest with the vodka in a jar, seal tightly, shake and store in a dark place for about 2 weeks, shaking the jar once a day. Then taste. If the flavor isn’t to your liking, let it go a little longer. 

After the flavor meets with your approval, make a light syrup by combining the water and sugar in a saucepan over medium heat, whisking until the sugar dissolves; let it cool. Strain the vodka off the zest and combine it with the light syrup. (Store the zest in the freezer and use it to garnish various beverages or to flavor nocino). Pour the liquid through a coffee filter into bottles. Seal and store for 2 more weeks before drinking.

Fill a large jar with the lemon pieces (as many as you can fit in) and pour the vodka over them. Close the jar, shake, and store in a dark place for about 2 weeks, shaking the jar once a day. Then taste. If the flavor isn’t to your liking, let it go a little longer. 

Combine the water and sugar in a saucepan over medium heat, whisking until the sugar dissolves. Strain the lemons from the vodka and set the vodka aside. Put the lemons in the saucepan with the light syrup; bring to a boil, then reduce the heat and let simmer for 5 minutes, occasionally pressing on the lemons to release the last bit of juice. Remove from the heat and let the syrup cool, then combine with the vodka. Pour through a coffee filter into bottles. Seal and store for 2 more weeks before drinking. 

Store limoncello in the freezer so it can be served ice cold without requiring actual ice, which would dilute the taste and silky texture of the beverage. The high alcohol content prevents it from freezing.