I wondered the same thing myself. I was reading Book 4 with the near certainty that Ferrante was going to blow all of this up in the Epilogue and point to some kind of irrefutable proof that Lenu had invented Lila. That this foil she had created, which had driven her to survive a very rough childhood (almost like an imaginary friend), had been incorporated so completely into a young Lenu's mind that she (Lila) had continued to drive Lenu during her adulthood and at every stage, to be more and more successful. Lila is the imaginary friend who never went away. That is why Elena is always attributing her success to the "sparks" that "Lila" gave her during their conversations, to "Lila"'s thinking and "Lila"'s influence. These inspirational articles and fantastic pieces of writing almost cannot come from a normal mind, but the product of someone who thinks very differently; Lenu attributes all of this to "Lila".
Lenu and Lila even both love Nino; in Book 2, in Ischia, "Lila" could almost have been living out Lenu's fantasy of attracting Nino and being with him, while instead Lenu is being groped by Nino's father. Her mind is split, or, in other words, she is of two minds - one is experiencing the cruelties of her bitter reality (Lenu), and the other is experimenting with different ways of thinking and living (Lila).
But in the end, it seems like this is not so. Yes, Lenu was manipulated throughout her life by Lila, as proved by the return of the dolls which were the deceit upon which an important cornerstone of their friendship was built, but Lila was a real person. They were each other's "brilliant friend", a complex love and rivalry more enriching and involving than any romantic connection or family bond could ever be.
Lenu and Lila even both love Nino; in Book 2, in Ischia, "Lila" could almost have been living out Lenu's fantasy of attracting Nino and being with him, while instead Lenu is being groped by Nino's father. Her mind is split, or, in other words, she is of two minds - one is experiencing the cruelties of her bitter reality (Lenu), and the other is experimenting with different ways of thinking and living (Lila).
But in the end, it seems like this is not so. Yes, Lenu was manipulated throughout her life by Lila, as proved by the return of the dolls which were the deceit upon which an important cornerstone of their friendship was built, but Lila was a real person. They were each other's "brilliant friend", a complex love and rivalry more enriching and involving than any romantic connection or family bond could ever be.