This discussion may contain spoilers!
So we know that Faith was covering for Lily the night Bigby encountered her at Woody's apartment. And we know that Lily was glamoured to look like Snow when she died. So that made me think, did the killer necessarily know it was Lily when they killed her? What if Lily took one of Faith's clients in exchange for her taking Woody?
Think about it. Faith stole something from the Tweedles' employer, who is very likely the Crooked Man. We probably won't know more about what his game is until Episode 3, but it sounds like he's keeping a lot of folks in Fabletown in his debt. Dee and Dum are seen searching every place that Faith had been on the day of her murder. Dee is seen at Faith and Lawrence's apartment and at Woody's apartment. We also find out in Episode 2 that someone had searched the jewelry box and makeup case in Faith's cubby at the Pudding & Pie--probably the Tweedles looking for whatever she stole.
What if they show up at the Open Arms Hotel expecting to find Faith? Because Lily is glamoured, they don't realize they've got the wrong girl until after they've already killed her. So they dump Lily's body in the river. Maybe Dee is giving Dum a hard time about targeting the wrong person, and Dum responds by saying, "Stop laughing at me." Then after they kill Lily, they catch up with Faith for real after her appointment with Woody. But she doesn't have what they're looking for on her, so they start searching everywhere that she's been.
Of course, that doesn't explain why the heads were left outside the Woodlands. In Episode 1, Bigby can theorize that Faith's head was left there as a message. It could be that Faith had the chance to pass along whatever she stole to someone in the Woodlands. Or perhaps it's just a threat to someone else in the Woodlands. Like Crane perhaps. Or maybe Bluebeard. What was he doing interrogating Bigby's suspect anyway? That's not his job. He's not officially associated with the Fabletown government. So why's he so gung-ho to find the killer? Unless maybe he knows that he's the one being threatened. I don't know. Honestly, this might be the part where this theory falls apart.
It's hard to say what's going on for sure without knowing what it is Faith stole. It can't be the donkeyskin cloak because Toad says he offered it to Dee and he wouldn't take it. I thought it might be the ring, but that seems unlikely as it was in her mouth when her head was found. That doesn't seem like something the killer would have just missed. There are a few other accoutrements generally associated with the Donkeyskin story that haven't been mentioned yet in the game. But if the Tweedles searched Faith's jewelry box and makeup case, that would seem to suggest that whatever she took is something small enough to fit inside one of those containers. Maybe another black market glamour case? There were people speculating that the one Crane is shown leaving with in the Episode 3 preview is a different one than the one found on Lily's body since Bigby still has that one at the end of Episode 2.
In any case, whatever Faith stole seems like a key piece of the puzzle that's still missing. Still, since Lily was glamoured to look like someone else at the time of her death, it does strike me as being very possible that whoever killed her wasn't actually after Lily. What do the rest of you think?