I wonder if the nameless black company employee who took over Lunaria said all that to Mythos because she doesn't really feel like she's living as Lunaria now, for good? After all, she's living a game scenario, with those repeating interruptions from the UI. They even stop time until she chooses one, exactly like it would be in such a game. That might make her feel like she hasn't really become Lunaria, she's just playing a game in her body, to save her and punish those that doomed her. It was pretty much her dying with in her original world, before I-Beam-kun killed her.
Otherwise there would have been no need to agree to anything Mythos was insinuating. She could have simply told him to try living under oppression and torture in his own home, to see if that doesn't change a person. Nothing else would have been needed. So, for her to willingly tell anything much, it's just because she feel obligated to do that not for her own sake, but for the dead Lunaria's sake.