When you get Character A and Character B opposed as to what is the truth, then the sparks will fly, the story will take off because it will have to be resolved one way or the other. Which one was telling the truth?
If it is a case there is no outright lie, but a case of seeing something from a different perspective, one of the characters is going to have to shift their position to be able to recognise that, otherwise there is no resolution. The story there is how they come to do that.
If there are outright lies, do the characters responsible get away with them? If not, how are those lies exposed and stopped? If they do get away with it, what are the consequences, especially for those who tried to combat those lies? (There will be some - at best, the truth teller can expect the liar who got away with it to "trash" them, possibly literally).
It is interesting in coming up with the lying character to find reasons for them to do this. The reasons have got to be good (at least from their viewpoint, they have to be able to justify their stance to themselves, otherwise they'll never go through with it). Sometimes, of course, a character may genuinely believe they are not lying but are. They have been given or inherited from someone (especially family) false information that is being challenged. How do they react to that? Great story possibilities here.
Truth and lies are crucial to fairytales too. We have to believe Cinderella etc is telling the truth - that they really are the good guys - otherwise the whole thing falls apart. This is one aspect of fairytales I love - it is clear what is right and what is wrong (usually) and I feel that is why they they make such sense for children. When you already know life isn't always fair (and kids do know fairly early on), to read tales where wrong is always righted is a great comfort.