I've been following this thread and I think it's necessary to point out that I think Hermione would be very much understanding of an eating disorder. Disordered eating is a control problem linked inextricably with depression and anxiety, and from what we know about Hermione, she is a veritable control FREAK.
Many times, an eating disorder has nothing to do at all with your body image, but rather the fact that you have so little in your life that you have control over. The way you look is something that is most definitely yours and something that you have direct control over.
In my early teen years, I had a lot of disordered eating and a binge/purge cycle. I think it's incredibly important to make sure that you explore the psychological aspects of this disease (because it is a disease) and remain sensitive to the actual causes. I think Lily's aunt Hermione would be a great support system and advocate for her, because she so intimately understands what it's like to need control, even if that's not the method she herself chose when she was in school.
Feel free to PM me if you want help writing the disease, I'm very forthcoming about my experiences
It's sounding like you're started to get some good points that have led to Lily's anorexia. The only thing I would advise is to make sure there's a lot in her background, since it is a gradual thing. Little clues from her history that only get linked to the anorexia in hindsight. I would find it really hard to believe that one day she went from fine, to completely struggling with anorexia the next.
That is exaggerated, but do you get what I mean? Anorexia is the type of thing that is really complicated, and can have many degrees of seriousness. It's really easy to not see the early stages. Sufferers are able to lie pretty well, saying they ate earlier or just started a new exercise regime.
And just remember, like Carole said, anorexia isn't necessarily about being thin, although it often starts out that way, but about being in control. Sufferers feel like they don't have any control unless they stick exactly to their precise eating and over-exercising habits.
It's a tricky topic to tackle, but I think you're definitely approaching it in the right way.