Spoiler :
1. I don't think she knows, it's not really mention in the novel, but I think she's really did think that she's noble. She has a bit foresight, she didn't have the full story how the future goes, so maybe she's only saw a bit after she dies.
2. Lilian's appearance is more from her father's side. The butler mention how she looks similar to her father when he's a child. And her hair is going to be blonde later on, I forgot from which family, but there's that. This is where I felt frustrated, because the head maid can see and fully believe that she's the real deal, but the father is so blinded by his wife appearance that he didn't see that Lilian is similar to him.
3. It get out in the end, but even Lilian is still didn't believe it. Because it's not DNA test quality fact. Just a circumstance fact, the first 'moon child/saint' (I forgot what they called in this novel) can sense that whenever another one of them is born or die because the power is divided between them.
They said the power is hereditary, and the first 'moon child/saint' is still on earth for a mission, but it doesn't mention about Lilian's grandmother. So, I don't really know. It's kinda open ending on that.
Oh, her father already felt that she's his child after the fake child incident because he get ripped apart by the head maid.
And I think, the fact that Lilian never really believe it, it's the punishment for him.
Okay so
1. If swan has foresight and knows she’s not the real daughter, why lie to Lilian and say she is?
2. This isn’t how genetics work. Why does Lilian look nothing like the parents? I get swans appearance changed, but did Lilian’s change too?
3. Does Lilian ever find out she’s the real daughter, and if so, when? Same for dad