If the moonshine drink is 64-proof or higher, it doesn't need to be refrigerated. This Lemonade Moonshine Cocktail must be refrigerated because it's only 15-proof and contains lemon juice. Store in it a tightly closed mason jar in the refrigerator and use it within two weeks. If you make 30-proof lemonade moonshine, you can store it for up to four weeks in the refrigerator.