Scrub the limes with a vegetable brush, wash, and pat dry. Peel the limes using a potato peeler, taking care not to get any of the white with the peel. (The white pith will make the liquid bitter.)
Put peels in a large jar with a tight-fitting lid. Add the alcohol. Close tightly and set in a cool, dark place (free from sunlight) for 7 days.
When the 7 days are up, remove the peels and strain the mixture through cheesecloth 2 or 3 times until the liquid is clear.
Combine the sugar and water in a small saucepan. Bring liquid to a simmer. Heat until sugar completely dissolves and is clear. Add lime juice and stir. Let cool. Add the infused alcohol. Store in the freezer until ready to serve.