Sad as it is, I have female friends who actually like Lena Dunham; all of them white, liberal and suburban, and most of them younger than me too. Onw of them even watches Girls, or at least did. I stopped talking to her about it after she half-heartedly defended the pitting rocks in her sister's vagina thing.
I have a pet theory that the real reason for her popularity, and Amy Schume's, is that women are catty, and like seeing women who are less attractive than themselves in every single meaning of the word. They don't really care about the whole 'body positive' crap or breaking down stereotypical gender roles. They want to see a fat slob with no sense of fashion or boundaries because it gives them the smug satisfaction of being better.