Mentiría is the conditional form of the verb mentir (to lie), meaning "I would lie". It's a powerful word because it sets up a hypothetical situation, hinting at a truth the singer is reluctant to admit.
In the song, the artist sings, "Te mentiría si no te digo que a tus brazos de nuevo volvería" (I would be lying to you if I didn't tell you that I would return to your arms). This reveals a deep, hidden desire, making the word incredibly enticing and central to the song's emotional conflict.
The title is the joke. He spends every verse telling her he's fine, and the chorus admits that's a lie: "Que te mentiría / Si no te digo que a tus brazos de nuevo volvería" [That I'd be lying / If I didn't tell you I'd go back to your arms again]. His proof that he's moved on is a list, "La noche, los tragos, la gira, los ceros" [The night, the drinks, the tour, the zeros], where "los ceros" means the zeros on his paychecks, so he's bragging about money too. Then one line wrecks it: "Pero pasas enfrente y siento que muero" [But you walk past and I feel like I'm dying]. Notice "decís" in "le decís lo mismo a diez personas" [you tell the same thing to ten people]. That's the Argentine "vos" form, a giveaway that this is cuarteto from Córdoba.
He isn't a clean victim either. "Y que podrás estar con otro si sigues siendo mía" [And that you can be with someone else as long as you're still mine] is a pretty cheeky deal to offer, and he follows it with "¿No era eso lo que querías?" [Wasn't that what you wanted?], throwing her own terms back at her. The second verse is pettier still: he heard she's happy with someone who fills her "alma vacía" [empty soul], the exact phrase she used to say about him. It's a sad story played at dance tempo, which is how cuarteto likes it.