When faced with clues regarding The Tyrant Star, wich type of Lore is best suted to use to see if the Acolytes know anything about it?

Scolastic Lore: Legend?

Personally, I would say the following three would work:

Astronomy (at a -10 penalty)

Legend

Occult

But I could also see Forbidden Knowledge (Tyrant Star) being a new and useful skill being made, if the Tyrant Star is a big part of your world. It certainly will be in mine, and I am using such a home brewed skill. (However, I am actually calling it Forbidden Knowledge (Hereticus Tenebrae), as I prefer the name.)

I would use Scholastic Lore (Legend) for the bulk of the information, and allow some additional information with Forbidden Lore (cults) or Forbidden Lore (the Inquisition). I'm basing this on the Tyrantine Shadow Agent alternate career from the IH, which is basically specifically for knowing stuff about the Tyrant Star

Several of them I would say. The Tyrant Star is such a big thing in the setting (even if its hidden) that no single talent should give solid info on it, instead each type of knowlage should give you one piece of the puzzle.

For example, knowlage of cults could give you info about cults worshiping some some mystic black star. Legend could give you information about the prophecies. Knowlage about Calixis itself might give you hints of planets that where destroyed a mysterious apperance in the sky, and of course knowlage of the Inquisition can give you info on the Tyranites, The more facts and less rumours you get the more you are leaning to forbidden knowlage rather than common or scholastic, and the more of them you have the more you will be able to piece together a more accurate picture.