Ahh lying! As confusing or uncomfortable as it might be to realize that your kid is fibbing, it's a pretty normal developmental bit. There is theory that it is one of the signs that a child has learned that her feelings and expressions of them are in fact separate from her parents. I know that doesn't make it feel any better though. lol
So then what? I think understanding the reasons for lying is really key. We (people in general) lie because we are afraid of something. Punishment, embarrassment, etc. Or perhaps we want something? Lying also happens because we want to seem more interesting or funny to others, or to be "in" with whatever they are doing or telling. Very young children also struggle sometimes with seeing the difference between fact and fantasy clearly. Story telling was my son's big thing when he we little, and boy was he ever convinced and convincing sometimes. ;)
With the lollipop thing it's pretty clear what the motivation was: candy! She's aware that her parents control access to the goods. I think you can say, "Let me just ask mommy if she still thinks a lollipop is okay right now before we get one." This way she understands that you two are going to be on the same page. If you wanted to address the dishonesty directly you might say, "You wanted the lollipop so you said mom said it was okay to have it. She didn't really say that it was okay though." You can go on a little bit about how saying something happened or that someone said something that really didn't, etc is called lying."
Here are some links too: