Are you trying to find a reason to believe that Lucas is Ellie's father and not the MC? And remember the backlash after Ch1 was released, everyone thought exactly that, "Lucas and Olivia had Ellie", "Olivia and Lucas betrayed the MC" and "This needs the NTR tag". So why can't this not also be a hint from the dev to the player, where the dev says "hey guys, Olivia had nothing with Lucas and also nothing with anyone other"? And seriously ASKED yourself from where Nova knows who Mr. Kim is! Nova has more knowledge about Olivia and everything else, than she lets us know. It's obvious. She could have phrased in a other way, something like that "nobody is touching Olivia". With present tense it would have made sense to believe, Olivia wasn't seeing anyone at the moment but the MC. But she says it in past tense. It's a BIG difference. But if you want to believe something else and want a discussion about it, maybe even how this game contains NTR, fine. But search for someone else and turn it into a private discussion.
He has no picture of Lily, look precisly, then you would see that he has a picture of Olivia and one of the MC together with Lucas. I mean take a look for yourself, and tell me where you see Lily:
I think you confused yourself.