Rowling didn't do as much with the James-was-a-bully as I would have liked to see. I think it was mostly there to support Snape as a good guy, as it is used to explain his hate-on for James, and to present Snape more sympathetically. There's a shading of "boys will be boys" that I sure don't like.

HP isn't what I think of as a lineage story because what makes Harry famous is that he's the Boy Who Lived, rather than being the Son of James & Lily, and that's a slight perspective shift that is, I think, what makes HP different. But him being an important person at all is also what keeps HP from fitting my trope in any more than a passing way. I sometimes wonder what HP would have been like if Hermione had been our central character. (It would be a lot more like an anime plot.)