Kids will try to get what they want, including that piece of candy. If it is so important to a kid to have the candy (or whatever it is that they want) that the child is willing to lie about it to get it, maybe it would be helpful for the parents to think about their reasons for not wanting to help the kid get whatever it is they want. I think there are better ways to get what a person wants, than lying, and maybe this is a more productive way to approach the lying issue. If the kid wants the candy, and the parents don't want hir to have it, can the kid come to the parents with hope of discussing the issue and finding a better solution than lying about it? Maybe the parents can come to respect the kid's right to eat what kid wants, and they can all research and learn together about different ways of eating and nutrition information and the many conflicting theories about food and so on.
Lying is a solution to a problem, like uh-oh, I'm about to get in trouble, how can I get out of this? Fear of the anger of a parent (authority) is a powerful motivator to lie. How can the parent and child have a relationship where the child does not need to fear the parent? Or is that what the parent wants, child to obey because of fear? I guess that is an individual preference, but it seems to me that if there is going to be obeying and fear, there will also be lying, by way of self-defense.
I remember something in an Eda LeShan book- something like, 'When Your Kids Drive You Crazy'- where I think she made some sense in talking about lying. I haven't read it for years, maybe I should go find it and see if I still agree with her!