(I don't own this headcanon)
This is such a perfect idea! Whether this was J.K. Rowling's intention or not, it fits so perfectly. Snape must have seen the similarities between Hermione and Lily.
Hermione was originally supposed to be with Harry, which means that they were basically going to be another Lily and James (except Hermione didn't hate Harry at first). I am happy that the plan was changed and Harry ended up with Ginny, and Ron ended up with Hermione though. I think it just fits better.
But really, just think about it. Hermione and Lily were both really smart muggleborns who loved learning- which supports the idea that people who didn't grow up knowing about their magical abilities appreciate going to Hogwarts more like I talked about a bit here- and like the head canon said, they were both friends with a Potter. They weren't similar enough that it was like J.K. Rowling was writing the same character twice, but enough of their characteristics were the same that it would make sense for Snape to compare them- thus hating Hermione who reminded him of Lily.
There was another head canon floating around that sort of expands on this idea:
The reason Snape hated the Golden Trio so much was because together they made Lily. Harry had her eyes, Ron had her hair and Hermione was a smart muggleborn.
This post also makes me feel bad for Snape though, because everyday he had to look at these students who reminded him so much of the girl he loved. I can imagine if I was in his situation, I wouldn't really like the Golden Trio either.
My biggest wonder is whether J.K. Rowling did any of this on purpose. When she wrote about Lily did she base them off the Golden Trio (or vice versa)? And was that part of the reason she made Snape hate them, even if she didn't mention it in the books? It's not crazy to think she did it on purpose, since there was a lot of stuff she knew about that she didn't explicitly say.
Some people say that Snape just hated them because Harry was the son of James, they were Gryffindors and all that, but I really think that there was more to it than that.
Snape's love for Lily was something that ran deep, that he never forgot. None of us will ever forget when this happened:
Yes I just brought that up.
I'm curious though. What do you think about these theories? Do you think they make sense? Let me know in the comments!
I hope you have a magical day/evening/night,