Pour vodka into a clean glass jar.
Wrap lemons in cheesecloth and suspend over vodka (using the twine to secure them).
Seal tightly, and let sit undisturbed (in a cool, dark place) for one month.
After one month, discard lemons, then add syrup and the fresh zest of two new lemons.
Let sit for 15 minutes, and strain through a fine mesh sieve (or more cheesecloth).
Chill and then drink up.
