One is a Scientist, they are always correct about which statements are true and will always tell the truth.
Another is a Psychiatrist, they like to test people by lying and seeing their reactions - however, they are misinformed.
The remaining one is a Lapidary, they will always try to tell the truth, but they are also misinformed.
They receive information (or misinformation) about each other's behaviours and make the following statements:
- Keir: Lucy is misinformed.
- Anya: I am not misinformed.
- Lucy: Anya is the Psychiatrist.