I'm indifferent to lip size. If there was a choice, I suppose I'd prefer visible lips but my current SO is on the opposite extreme with very tiny lips that really aren't visable. It's no big deal either way.
Now, having been in a relationship with a woman who had large lips, I would note that she related to me that she suffered quite a bit of teasing in her junior years because of it. I don't know how common that is today anymore -- I'd never heard of it before her (or at least had never thought anything of it) -- but she claimed to have been labelled a "slut" in high school because of her lips. She definitely had latent issues with the appearance of her vagina because of those large lips as long as I knew her.
I doubt there's any therapy for it. The woman in the original post, I'm guessing, probably had similiar experiences to that of my former SO. Based on the former SO's stories, it is most likely that other women caused her insecurity about her vagina's appearance. I'm not sure, but I doubt a lot of guys have any signifcant preference either way -- though if anything, it would probably be a preference for visible lips.