At this point the only things we can assume are true about Lila are things we find out while she thinks she's unobserved. So we know she has a secret lair in the Paris catacombs where she's been gathering information related to the Miraculouses and their wielders and their minions. We know she was in the Agreste mansion in the S5 finale at a time when (1) there was a big hole from the foyer to the creepy coffin basement (2) the Butterfly Miraculous fell off the catwalk and Marinette couldn't find it afterwards. We know she has known who Monarch is for longer than we have known she knows who Monarch is; we also know she knows Kagami's mother has been working with him knowing he's the resident magical terrorist for at least as long as the Tsurugis have been in Paris, and quite possibly as long as the Tsurugi company has been doing business with the Agreste company. And we know she discarded the Lila Rossi identity altogether, or at least the wig she was wearing all series until that moment.
And that's very nearly everything I can think of that we know about her that doesn't require wondering to what extent it's a lie.
We know Marinette's school isn't the only one certain that Lila, under some name, is a student there. (The Lila design in the controversial blorbos bracket is known as Cerise to students at that other school.) We know of three different women, each of whom is certain Lila is her daughter, who don't seem to know about each other. We know Lila first arrived in Paris shortly after it hit international news that there were Miraculouses active in Paris. (How shortly, we have to take sides in the great timeline debate to figure out. Dear canon: Adrien has had two birthdays and a second start of the school year between Origins and S5; Origins is the start of his last year of collège; the end of S5 is the end of his last year of collège; pick two.)
Since we don't know how long Lila has known Gabriel Agreste is Hawkmoth, we can't be certain Lila only ever wanted Adrien as a pathway to fame and fortune with a side bonus of getting one over on Marinette and/or on Ladybug.
...
Honestly the only thing that makes sense to me at this point is, Lila is a comic book villain who is significantly older than she looks, who came to Paris at the end of S1 because she found out there were Miraculouses there, and who possibly radiates magic of some sort that makes people a little more inclined to believe whatever she tells them.
