Personally I don't believe she's hiding herself at all. You may call me a blind stan, delusional even, but I think she's 100% herself in everything she does. Fakery is very easy to notice, and I definitely don't see it in Lana Del Rey at all. Old Hollywood glamour style is just what she likes, nothing else (and personally I'm quite in love with it too, tbh).
And what comes to her lyrics, I think those references to Marilyn Monroe and Elvis and what other are just some metaphors she uses. It doesn't make her any less true popstar than any other singer out there. Personally I love the lyrics she writes. It's her very original style and it's also one of the reasons why I love her music. Her lyrics are awesome and I feel that they are honest. If they weren't, there wouldn't be so much pain heard in her songs.
That's how I feel about this.