I'm not sure if you're referring to the lemon drops candy or to the juice of a lemon, but both would work the same way. Apples and some other fruit turn brown because they contain a compound that is oxidized by oxygen in the air. The ascorbic acid in lemon juice and lemon flavored products prevents this from happening by reacting with the air first. Coating the cut fruit with an ascorbic acid solution creates a barrier that protects the fruit from oxidation until all of the acid is oxidized itself. Fruit Fresh is a product containing ascorbic acid that's marketed for preventing discoloration of fruit.
Ascorbic acid is vitamin C. You've probably heard that vitamin C is an antioxidant. Antioxidants protect cells from damage by reacting with free radicals, molecules that are strong oxidizers and attack cells. Free radicals are thought to play a role in aging, cancer and other illnesses.