When Harry accesses Snape's secret memories during the Occlumency lessons, he doesn't see the one of Snape being bullied. He sees one of a friendly interaction between Lily and young Severus, where Severus is clearly in love with Lily. After Snape throws him out, Harry asks Dumbledore if this is why he trusts Snape, which Dumbledore confirms. From then on, Harry defends Snape to everyone who questions his trustworthiness.
Only one year later, when he sees the memory Slughorn modified, Harry realizes there was something wrong with Snape's memory.
When he goes to Dumbledore to warn him, he is told that this sort of thing is common with oft revisited memories and Snape likely idealized Lily a bit after her death. Nothing to worry about.
Only after Voldemort's defeat does Snape admit that in truth, instead of him spying on Lily and ultimately befriending her, it was Lily who walked up to him and asked him to be her friend, and he loved her like a sister. Gaining a friend was the life-changing event that changed his patronus.
Before begging Voldemort to spare her, Severus convinced himself that he was in love with Lily, as that was the only way he could think of defending against Voldemort's legilimency. He then went on to imply to Voldemort that he lusted after Lily and wished to keep her as slave, but without actually saying even just one untrue word.
- Harry never goes to the Department of Mysteries and Sirius survives, either because Harry apologizes and Snape teaches him Occlumency, or because Harry trusts Snape after telling him that Sirius is in danger, so after getting rid of Umbridge walks back to the school and finds out Sirius was at home the whole time.
- but Harry still goes on an adventure that makes him befriend the people who in canon go to the Department of Mysteries with him
- Severus survives because Harry (or someone else) cares about saving him
- Harry finds out what Snape told Voldemort in his last battle against Voldemort, from Voldemort himself, and at first is very angry at Snape
- Luna explains to Harry that Snape must have lied to Voldemort, and why.