Asura doesn't need to lie. He's telling the truth, but since the police have no knowledge about the key, it sounds like he's lying. Plus they're questioning Asura after he got attacked, so they think his story might be from distress.
I felt relieved when the key didn't work on the police. Didn't want someone innocent going to hell.
Is this guy Raika's actual brother, or just someone claiming to be Raika's brother?