Random observation: Ladysuburu's emphasis, considering the OP, seems to be "outside the box" thinking. So what if the fundamental premise that the killer is a role consistently assigned to one of us is incorrect? I can think of some ways this might be true:
1. None of us are the killer and it's just LS messing with us. (somewhat unlikely given that the results of the lie detector day 1)
2. Every round, one of us randomly becomes the "killer" in addition our normal abilities. This may have happened to rust45 during the previous night, thus leading him to inadvertently kill his target in addition to his investigation. (This would match the results of the lie detector.)
3. One of us actually has the ability of assigning someone else to target the killing. I came up with this just based on the fact that rust45's investigation target died, and many of us targeted rust45 without an apparent result. In other words, someone has the ability of killing the target of their target. Candidates for this would be bmin, Rantai and me (and maybe Q). This would also match the results of the lie detector.
Anyone think that any of these theories is plausible?