This discussion may contain spoilers!
Which is mine, because there's NO WAY anyone else has thought of this yet. No sir. (If it's already been done to death, please let me know. Links would be nice, as I want to see what other people have thought of this idea.)
Sorry guys, I just don't want to read a billion theory posts, but I want to get feed back on my theory that I've been working on since episode three. I have read a few pages back of theory posts, but I couldn't quite buy in to most of them. So, here's what I think:
Faith killed herself in a plot with Nerissa and Lily to expose the black market the Crooked Man was operating to Snow and Bigby.
In episode one, after her encounter with Bigby, Faith realized that he's "not as bad as everyone says he is" and that he might not be as corruptible as Crane and just might be able to take down the Crooked Man. She knew that it would require her life, so she wrote a letter to Lawrence saying, "I'm sorry," that she planned to deliver later. She then went over to Lawrence's apartment to check up on him and found him dead from the gunshot (hence, letter was never sent). She called Lily and Nerissa over, her only two friends, and put together would they would do. (This is why some stuff was moved around in the apartment, such as the bed being folded up. Lawrence wouldn't have done that if he wanted the note to be found.) They could not tell Bigby and Snow directly because of the ribbon, but they could plant clues that would point them in the right direction. This is also why Nerissa checks up on Bigby's progress later, and even takes a risk by going to his office in an attempt to point him in the right direction. She is trying to make sure that their plan works and that her friends' sacrifices were not in vain. Faith killed herself by pulling the ribbon. Lily took Faith's ribbon, tied Faith's ring (which had her family seal) to the ribbon and stuffed it in Faith's mouth. (Because seriously, why on earth would anyone do that if they'd killed her? The Crooked Man and his goons had a good thing going with Crane, why mess it up with this?) Lily then left and planted Faith's head in front of the Woodlands for Snow and Bigby to find. (As a side note, it's possible that what Snow and Bigby thought were needle marks on Lily's legs were actually mostly healed punctures from the Woodlands fence.)
When Crane leaves the Business Office after being informed of the discovery of the head, he goes to the Pudding N Pie to pick up Lily. While there, he tells Vivian that a prostitute's head was found in front of the Woodlands. While Crane is busy with Lily, Vivian tells Georgie, who calls the Tweedles to investigate and find out what happened to one of his girls (they don't know at this point that this is a plot to expose the Crooked Man). Like any intelligent pimp, Georgie protects his merchandise from the Johns and if one of his customers is killing his prostitutes, Georgie wants to stop it. The Tweedles, thanks to Georgie, know which girls were where last night and they quickly figure out which one is missing. Dum goes to the Woodsman's apartment, Faith's last known customer, while Dee goes to Lawerence's place to see if anything happened there. (If you don't go to Lawerence's first, Dee assumes that Lawerence is dead and probably sticks him with the knife or sometihng to make sure, which actually ends up killing Lawerence.)
I believe that Lily killed herself just before Crane used her in his Snow fantasy. Looking at the blood pattern on the bed, it's obvious that Lily knelt down beside the right foot corner while Nerissa pulled the ribbon. It strangled her, which is why Beauty didn't hear anything. During the strangulation she clenched the top of the bed, locking some of the flowers into her fist. Then her head came off spraying the blood onto the bed. I think this because of the hand prints on that corner and the fact there's a pool in the middle of the bed, but no spray on the wall or headboard. The corner has two handprints an equal distance apart, which I think means someone else pulled the ribbon. Nerissa then planted the photo of crane that Faith stole in the closet and took Lily's head and placed it in front of the Woodlands. All of this was to plant more evidence and bring to light Crane's role in the black market.
Crane later showed up for his appointment to find a bloody mess and a decapitated body that looked like Snow. He ran and got the Tweedles or Georgie, who took the body and threw it in the river, laughing at Crane, likely making jokes that whores would rather kill themselves than sleep with him. When Crane got back to the Business Office, Snow was gone because she'd been called by Toad and Bigby was arrested by the NYPD. Crane began to fear at this point that it was Snow herself that was murdered in the room as payback. I don't think Crane was the one who found Tweedledee chained to the lamppost, as he would have let him go, and I don't think it was Bluebeard, as he would have interrogated him elsewhere. They either found Tweedledee together or he was found by Grimble. Crane then goes and gets Bigby and Lily's head from the NYPD using a spell from the Crooked Man's blackmarket. There's no way the 13th floor would have allowed the crafting of a spell like that. They would have just used Sleeping Beauty's curse as they have in the comics. Crane threw her body down the Witching Well to help get rid of evidence.
Crane realized that there was some sort of exposure plot going on he saw his stolen picture being found in the closet by Crane, he just incorrectly thinks the plot is to expose his Snow fantasies and to make it look as though he were the murderer. This is why when he is found at the Pudding and Pie with the Ring of Dispel he says to Nerissa, "I know you know the rest of the plan." He targets Nerissa and not Vivian because he knows Vivian works more directly for the Crooked Man and that Nerissa was friends with Faith and Lily.
All the rest of the story is not to solve the mystery of Faith and Lily's "murders", but is to uncover and deal with the fable black market. It's also to validate Bigby's evolution over the last several centuries from villain and killer to hero and protector.
Anyways, that's likely what happened to Faith and Lily. Also why Nerissa freakss out when Bigby moves to take the ribbon off, because she's seen twice now what happens when you do that. (And, if you believe the magic item exists, she doesn't have it with her.)
phew Glad to have this theory off my chest.
Oh, and King Cole isn't on vacation, he's probably in Bluebeard's basement. Or this was all HIS ruse to lure out the undesirable elements living in Fabletown.