Is there an adjective that means that something is part of the lore? The word "lore-friendly" means something isn't in contradiction with the lore, but it doesn't necessarily mean something was mentioned in the book. Is there a word that's specifically tailored to mean the latter? I can't think of a single word that means that, but I swear there's a word for it.
The word you are looking for is "canon". This means the object being discussed is accepted as part of the official lore. This is opposed to "non-canon" which means the object in contention had not been accepted as official for the moment (although sometimes it will get added later).
"Canon" means something has been confirmed by the author of a piece of media. "The canon" refers to everything that is canon. You can either say that something is canon or that something is a part of the canon. Don't confuse canon with cannon (the weapon).