Pardon, I don't have access to the books at the moment, so I was hoping somebody might have the answer.
While House Ex Miscellanea is a Society as a whole, what about the individual Traditions within it? Are any of them True Lineages or Mysteries?
Specifically the Children of Pralix. From what I recall of the write-up, it does sound like they try to behave very closely to the Founder Pralix's viewpoints, which leads me to suspect they are a True Lineage - only an apprentice trained by them can become a Pralician.
Hi! I think all of them individually might be considered True Lineages, if not for the fact that TL seems to be a term of honor for the HoH TL, and they might scoff at these "hedge lineages" calling themselves by that term. But as a House, they are all a Societates: Magi from outside the House join in, and only the Pralicians can be said to have been taught their magic by the Founder of the House, in a direct line. Although Pralix never joined House ex Miscellanea.
None of the ones on HoH:S are on their face Mystery Houses, although one can see how they might improve by creating a Cult. The Thessalians and the Damhan Duidsan are mentioned in passing, and one assumes probably have Mystery secrets of the Goetic/fully Infernal kind.
The Cult of Orpheus and the Seirenes are performers, so might benefit from a high Presence, and this naturally is useful for Mystery Initiations.
I suppose it depends on your definition of a True Lineage and a Mystery...
A lot of them have a Mystery Cult feel to them, but none seem to truly fit the Mystery Cult descriptor as they aren't going out and recruiting more; and I haven't seen any examples of people outside Ex Misc being able to go (example) just join the Pralixians or Cult of Orpheus. Rules wise, none of them have made mystery cult initiations, and some Ex Misc characters are not designed with a Cult look, since the non-Hermetic virtue you can chose as Ex Misc could be Wealthy or Magister.
As far as True Lineages, just anyone can join into the Ex Misc with permission, so they definitely fall among the Societates of the OoS... the individual Ex Misc lines feel like a mix between True Lineage and Mystery Cult, but without the actual benefits of either.
But I don't think this is a requirement, as much as it is a matter of editorial convenience. An ExMisc MC would need a more extensive writeup to make it interesting, with scripts and new virtues. Easier to just ignore the MC aspect of a tradition, and let players roll their own if needed. An Ex Misc Societas does not have that problem, but those tend to be larger. Easier to ignore an Ex Misc tradition and explain that it is tiny by having it act as a lineage.