I almost wonder if the writer for the Invisible History DLC was a different one from the main writing stable, because almost nothing from it is acknowledged here. Nothing about Hydra and Mikoto's past, nothing about Lilith's heritage aside from that family chart.
That's Lilith's profile on the left. You don't even need to be able to read Japanese--do you see the word ハイドラ anywhere in there? It ain't present. The closest thing to new information in there is the offhand mention that celestial dragons are a subtype of the Divine Dragons which created the world and they can move between dimensions. And something about them being unable to physically speak and communicating through telepathy, but I honestly can't tell if that only applies to Lilith or all of them because there's so little information.
This book feels like it was written by several different people who weren't speaking to one another.
I have absolutely nothing factual to support this, but I kind of suspect that the Lilith in the final game is the result of two different characters folded together. The fairy who's fond of MC and gives up their human form to protect them is a decently common trope on its own, and everything about Lilith in the main game exists only to justify the pocket dimensions of the Deeprealms and My Castle, meta concepts which are so divorced from the main story I'm pretty sure they're not even canon. You don't need a heavily-invested backstory to explain some ancillary gameplay mechanic.
Invisible History Lilith, however, portrays a totally different type of character who's woven into the backstory of the main conflict in a critical way. This is completely at odds with how the main story treats her. Nobody would write like this on purpose. Was it a retcon? A character cut and retooled into Lilith? I can't tell you, but something is off here.
Incidentally, I wanted to point out that that center concept actually isn't Lilith! It's labeled Celestial Dragon in the general sense. So they all look like koi, I guess?