I don't like her because I don't like her lyrics (on their own, they sound like Katy Perry song lyrics; very, well, not good) & the music does nothing for me. I think she has a nice voice, and her image doesn't bother me so much as the apparent intent to manipulate the audience into thinking she is "indie". She isn't, that's fine, but why pretend? Because that's the market she was trying to hook, since it suits her persona. That market will backlash harder than most because it's all wrapped up in "authenticity".
We were discussing her type on an INFP board (where some suggested she might be INFP; I didn't agree), and apparently "Lana Del Rey" is a persona created to be a caricature of what society expects of women (hence, the retro elements & bad lyrics, I guess). This idea is straight from Lizzie Grant's own words in some blog essay, or whatever it was. However, this essay struck me as a defense against the criticism of this persona, because I think the persona was meant to be some kind of hipster/indie Hope Sandoval (of Mazzy Star, and who is likely IxFP) kind of image. People saw through it, and now she's sort of backtracking & claiming something else. This persona adopting strikes me as INFJ. So did the essay itself, which explains the persona. Her persona now seems to be an ISFJ (prototypical woman - non-threatening), but I think it was meant to be ISFP. She failed at coming off as ISFP because of the whole authenticity bit. Once she was exposed as very contrived & trying to manipulate people, then it was better to claim another purpose other than "I was trying to cash in on an indie image & failed". In the interviews people posted, she seems to cop a total SiFe image now in what she says - very past-oriented, sentimental, focused on what is familiar, etc; yet her essay was notably more analytical, critical of society, focused on challenging people's attitudes, etc. It sounded kind of self-righteous, and like she thinks she's trolling people.
People don't like being trolled....