This is not to approach total honesty between people, although it could perhaps be used for that as well if some people desired this and would mutually consent to it. What I mean instead is using this for particular people who are known for mixing fantasies into their personal stories to the level that others can't tell what's true and what's not about their life/past experiences. Some readers who dealt with those type of people will know what I'm talking about. I have two friends who are like that.
The problem is that they are good people otherwise, but they like to fantasize, it's just part of their character and this quality becomes tiring after communicating longer with them, they don't admit their lies if you try to challenge some "facts", but instead will try to justify it further or present some more lukewarm alternative version of it. We could call this the Munchausen effect. There's a psychological condition called the Munchausen syndrome, although it's explicitly about exaggerating/imagining health problems, therefore a term Munchausen effect could perhaps be used for the cases that I've described.
I understand it would be complicated for a proposed app to debunk personal lies (in comparison to universally known facts) as well, but I think it could nevertheless be useful at least in some particular cases. Say someone claims that they worked in this extravagant company a few years ago, the app instantly checks the register of companies that were operating at that time in a specific location and finds out that such a company never existed.
I wonder how such people would react if the conversation with them happened in the presence of a proposed app. If the app was generally approved as effective they would probably avoid lying in the first place. The app could even be used silently in the presence of a particular person and compose a profile of him/her indicating a general trustworthiness level of their claims. The app couldn't confirm/debunk everything, but from the things that it could, it could quickly guess how prone to lying that person is.