This was a cool story. I like how you give this whole history to dementors with Severus getting told a story as a little kid and then have him pass along the knowledge to Lily. I also liked how you characterized Severus there with his feelings toward Petunia, feeling she should get put in Azkaban and stuff. That was so perfectly childlike in its ruthlessness because cutting off a doll's hair is not worthy of jail time, but is something a kid would think.
The reason for Severus learning the Patronus was cool and I liked it because he made it harder than it had to be to defeat the Boggart, but it pays off in the end.
His Patronus going through an evolution of forms is a neat idea and actually makes a whole lot of sense to me. People aren't stagnant. While a badger might have represented Severus as a kid, it wouldn't as an adult probably.
The later scenes where he uses it to warn Lily was neat too and I like how Lily realizes what happened and forgives Severus, having done some growing herself since the incident. It's just too bad she never got the chance to actually say it to him.
The end you chose is very fitting to and I liked it a lot.
There was one thing I saw:
"…Severus found had been used."
I think this bit is missing a word? "He" between "had" and "used" possibly? It seems like the most likely option.

I like this.

Fascinating evolution of the character and patronus. The wolverine fit very well with the fierce little loner he was as a boy (although it's sad that Lily was never a partner to him, not a mate, like Lily and James supposedly were, but a companion who always stood by him). The boar, another tough, sometimes dangerous beast, fit too.
Then of course, the iconic doe, because he never stopped treasuring the time when Lily was with him.
Very nicely written.