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1 liter of alcohol or 50 cigars, lol.You won't be able to purchase duty free during your layover at GCM since you're not leaving the Cayman Islands on your trip to Little Cayman.
IMO, you should absolutely, positively, with out question purchase purchase adult beverages in the U.S. before heading to any of the Cayman Islands. Between duty and shipping alcohol is quite a bit more expensive in Cayman than it is in the U.S. If you don't purchase it at the duty free in Charlotte, you'll have to pack any alcohol you bring in your checked bags. You may have to transfer anything you purchase in Charlotte to your checked bags for the flight from GCM to LYB, you'll have to double check on that. In my experience, the duty free at American airports is not appreciably cheaper than buying stuff at the local liquor store. Maybe a dollar a bottle or so cheaper at the duty free.
Here's a link to the restrictions on bringing alcohol into the Cayman Islands: "visitors 18 years and older can bring in duty-free either one liter of alcohol, four liters of wine or one case of beer (not exceeding eight litres) and 200 cigarettes, or 50 cigars or 250 grams of tobacco."
Customs Duty | Tips, Myths and More
You may have to transfer anything you purchase in Charlotte to your checked bags for the flight from GCM to LYB, you'll have to double check on that.