As the party makes its way back through the tunnel, Sirius notes that turning in Pettigrew will clear his name, and he tells Harry that he's his godfather. Awkwardly, he invites Harry live with him, and Harry leaps at the chance. Soon, they reach the opening and Crookshanks stops the Whomping Willow while everyone steps out. As they make their way towards the castle in the dark, the clouds shift. Snape's body runs into Lupin, Pettigrew, and Ron, who all stop suddenly. Lupin goes rigid and starts to shake. Sirius tells Harry and Hermione to run and then leaps at Lupin in his dog form as Lupin transforms into a werewolf.
Remember that Snape was taking Lupin the Wolfsbane Potion when he discovered the Marauder's Map; Lupin isn't safe at this point. Sirius's leap towards Lupin shows that now that his group of friends is expanding to include the next generation, he understands that it's his responsibility to keep them safe, just as he once kept the residents of Hogsmeade and other Hogwarts students safe from Lupin.
Lupin and Sirius rip at each other violently and Harry only stops watching when Hermione screams. He sees Pettigrew grab Lupin's wand, knock out Ron and Crookshanks, and then transform and flee. As Lupin races into the forest alone, Harry yells to Sirius that Pettigrew transformed. Sirius runs off after Pettigrew. Hermione and Harry approach Ron, who's alive but seems not to recognize them. In the distance, Harry hears a dog yelping and both he and Hermione run after Sirius. They find him at the lake, back in his human form, with dementors closing in on him. Harry thinks of living with Sirius and starts to shout "Expecto Patronum."
Now that Harry knows the truth of what happened twelve years ago, he also feels that it's his responsibility to fight for the truth and save Sirius's life. This again shows Harry truly understanding that he needs to take justice into his own hands and, in this case, fight the ministry by taking on the swarming dementors. However, it's also important to remember what Hagrid said about the dementors: they don't care who's guilty, which suggests that Harry might be in danger.
Hermione joins in, but she's too afraid to be effective. She collapses as silvery wisps come out of Harry's wand. Harry collapses as well and watches a dementor approach and lower its hood to expose a face with only a mouth. Harry's Patronus dies as he starts to hear Lily scream. The dementor grabs Harry's neck but before it can administer the Kiss, a silver light appears and the dementor drops Harry. Harry watches an animal chase the dementors away and then sees somebody welcome the animal. He faints.
Notice that the narration doesn't mention what the animal is or who Harry sees across the lake. This suggests that Harry will need more time to fully understand what's happened and come to an understanding of the truth. When the dementor tries to kiss Harry, it reinforces that the dementors, like the Ministry, aren't to be trusted.