Protagonist had her soul travel to another world, so her entire identity is basically a lie, as she pretends to be the daughter of a noble.
In this one, it's reincarnation, so the protagonist doesn't tell anyone he's a reincarnator (in the same world though), which also entails the reason for why he's reincarnating in the first place, as he's not human. In that regard, there's a lot of liars in the story - everyone who's the same as him would lie about their reincarnations.
Another secret within the story is the death of the twin sister of the protagonist (his "real" sister, as I said, he's not actually human). She was killed, but it was never solved who did it (though everybody knows, they just never speak of it).