Quite possibly, your just not getting lucky. I know i was stuck for quite a few in-game days looking for Lyx. But i dont actually know if Lux will appear before Claire does again, which might be stopping you from finding Lyx, however im not sure myself if thats the case.
If you havent checked out Lyx's cabin, that is a good place to start. If you have, then i think she is hiding around the manor somewhere, or is in the city. Kinda how she was in the previous act, just hanging arojnd certain POIs and observing people.
as for Claire, I know progressing her is related to doing as much as you can to fight the organization. I'm not certain, but I think Jessica knows a thing or two about finding Claire. Don't quote me on this though its been a minute since I've had to do this