There's a theory going around that swan was lyla mother all along
I think that's the theory in the novel too, because the holy power is the only reason for Swan's existence. Because she's supposed to be dead not long after she came to orphanage.
And because the holy power came from Lilian's mom, it influenced her appearance, and her attitude too because of the foresight power she gain. But it's not that strong, so she's only get a bit sight surrounding her own death.
Is that the reason why she doted MC and why she's looking young if she's the mother?
No, she's not her mother, but she has some memories and foresight of her mother. She's still a child, but unconsciously act like a mom.
It's still suspicious, maybe swan knows that she's not the real one, that's why she's making sure before she died that mc will be the one to go