How did Lily know about the tunnel under the Whomping Willow?

Question

From Harry Potter and the Deathly Hallows:

“They don’t use Dark Magic, though.” She dropped her voice. “And you’re being really ungrateful. I heard what happened the other night. You went sneaking down that tunnel by the Whomping Willow, and James Potter saved you from whatever’s down there—”

However, no-one knew about that tunnel!!

And also, Lily claims to have not known Lupin was a werewolf, yet she knew something was "down there" - even though all the shrieks came from the Shrieking Shack and nobody knew that the Shrieking Shack and the Whomping Willow were connected.

So how did Lily know about the tunnel and that there was something down there?

Answer 1

Lily didn't know the whole story, just that something happened.

She clearly didn't know that it was a werewolf, since she didn't seem to even consider that the theory that Lupin was a werewolf could be true.

“The intensity of his gaze made her blush. ‘They don’t use Dark Magic, though.’ She dropped her voice. ‘And you’re being really ungrateful. I heard what happened the other night. You went sneaking down that tunnel by the Whomping Willow and James Potter saved you from whatever’s down there –’

Snape’s whole face contorted and he spluttered, ‘Saved? Saved? You think he was playing the hero? He was saving his neck and his friends’ too! You’re not going to – I won’t let you –”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

She seems to think that the Marauders were totally innocent in it, that James saved him from a creature that had no connection to him. She mentions his (correct) theory that Lupin is a werewolf, his attempts to figure out where the Marauders go at night, but doesn't connect them with what happened at the Whomping Willow.

It's possible that James or one of the Marauders told her to impress her.

The way the story got to Lily, it seems very flattering to James Potter. James, though he hated him himself, knew Lily was friends with Severus. It's likely that he both wouldn't want to have the real story get back to Lily about how they endangered him by letting him stumble upon a werewolf, and would want to impress Lily. So, it's possible that he or one of the other Marauders told Lily how James heroically saved Severus from the creature he encountered while snooping around, making James look good and Snape look bad. In addition, he'd probably get "credit" with Lily for saving Severus despite James's obvious disdain for him.

Answer 2

Lily had heard what happened (quoted in the passage in question), from sources unknown*):

Snape had already shared with Lily that he thought Lupin was a werewolf:

"..every month at the full moon?", said Snape. "I know your theory," said Lily

Some further speculation would be that Snape himself had told her there was a tunnel, that he had seen Lupin go into it, and would be quite pleased to tell Lilly that her Gryffindor classmates, that he disliked so much, were up to something suspicious and have proof to back it up. From the same passage:

"They sneak out at night. There's something weird about Lupin. Where does he keep going....I'm just trying to show you they're not as wonderful as everyone seems to think they are."

Additionally, in Harry Potter and the Prisoner of Azkaban, Lupin explains what happened with Snape, James, Sirius, and the tree:

"Severus was very interested in where I went every month," Lupin told Harry, Ron, and Hermione. "We were in the same year, you know and we -- er -- didn't like each other very much. He especially disliked James. Jealous, I think, of James's talent on the Quidditch field....anyway, Snape had seen me crossing the grounds with Madame Pomfrey one evening as she led me to the Whomping Willow to transform. Sirius thought it would be - er - amusing to tell Snape all he had to do was prod the knot on the tree trunk with a long stick, and he'd be able to get in there after me. Well, of course, Snape tried it.

From these passages, we can see that Snape knew something was up with Lupin. Snape saw Lupin escorted to the tree. We can assume that Snape was somewhat free in talking about it (or at least confronted the Marauders with the information) as Sirius decided to tell him, essentially "you wanna follow him down the tunnel? Go poke the knot on the tree and see what you can find out."

Since it was clearly common knowledge, Lily had heard that Snape was in danger at the tree, and saved by Potter, it isn't unreasonable to assume then that she knew or assumed the tree was dangerous, and that there was something under it, since that was what Snape was trying to prove

*see Dumbledore's quote in book 1 about some secrets not staying secret among the student body: "What happened between you and Professor Quirrell is a complete secret, so, naturally, the whole school knows"