Alright now that I've had dinner and can think:
IMO the doctor must claim if he has protected either LS or Lybydose last night.
The reason for this is as follows. We currently have two people who claim to have been shot, LS and Lybydose. According to the setup, we have two players capable of shooting a player at night, the mafia and the SK. We must remember, however, that there is no guarantee that both the mafia and the SK shot someone during Night 0. Yes, it would be very foolish for them not to have, but it is still a possibility. If the doctor has protected one of the two, there is clearly something wrong, and it leads to the conclusion that one of the two are fake-claiming (of course, the doctor might be fake-claiming too, but for god's sake please don't do that.)
IMO the doctor must claim if he has protected either LS or Lybydose last night.
The reason for this is as follows. We currently have two people who claim to have been shot, LS and Lybydose. According to the setup, we have two players capable of shooting a player at night, the mafia and the SK. We must remember, however, that there is no guarantee that both the mafia and the SK shot someone during Night 0. Yes, it would be very foolish for them not to have, but it is still a possibility. If the doctor has protected one of the two, there is clearly something wrong, and it leads to the conclusion that one of the two are fake-claiming (of course, the doctor might be fake-claiming too, but for god's sake please don't do that.)