So I’m thinking here for a while that Lily knew Remus was a werewolf… It sounds almost like from the Prince’s Tale that her thoughts were “don’t ask, don’t tell?” I mean, I don’t think she would have embarrassed Remus by asking him after Snape presented his theory, but let us look at the evidence here:
Snape: They sneak out at night. There’s something weird about that Lupin. Where does he keep going?
Lily: He’s ill. They say he’s ill.
Snape: Every month at the full moon?
Lily: I know your theory,” she sounded cold, “Why are you so obsessed with them anyway? Why do you care what they’re doing at night?
Now, ever since I was a kid, I have always been interested in Lily’s character, and we’re told sooooooo little about her. This passage has interested me for a while. Just from the way JKR says Lily “sounded cold” when Snape brings up Lupin being a werewolf suggests that she does believe Lupin is a werewolf, is angry that Snape is bringing it up, but isn’t going to risking out him by agreeing with Snape because she likes Remus as a person. In her last bit of dialogue to Snape her attitude is basically “what does is matter if they’re sneaking out?” If Lily were the stick-in-the-mud!Lily here that a lot of canon loves to make her out to be, why not help Snape? The boys are sneaking out after all. But instead she’s just like “Does it matter if they’re sneaking out?”
My theory here is that Lily is pretty sure the boys are sneaking out, but guesses they are somehow helping Remus, and therefore decides the best thing she can do in this situation is act like she doesn’t know/care about the situation, especially given Snape’s obsession with the boys.