Scrub the lemons well. With a vegetable peeler, being careful not to remove the bitter white pith, remove strips of lemon peel. Place in a clean quart (4-cup) jar.
Pour vodka or Everclear into the jar, ensuring the alcohol covers the peels. Seal the jar. Let the mixture sit for from 4 days to a month. (See recipe Note.)
Line a sieve with a thin cloth and place the sieve over a medium bowl. Pour the contents of the jar into the cloth-lined sieve to strain the alcohol. Compost the lemon peels.
In a pot, combine the water and sugar over medium heat. Stir until the sugar dissolves, about 5 minutes. Cool and combine with the alcohol. Bottle and chill.
Store in the refrigerator for about a month or in the freezer for a year.
