The way I would handle a situation like this, would be that a player thinks up a single, fairly specific question, then rolls and factors in the character's Lore skill as well as applicable Arcane Library and character Aspects to determine the number of successes. The more successes the character has, then the more detailed the information the player gets with regards to the question, or perhaps the more quickly they collect the information.
A very good example of this sort of situation is from the second novel, Fool Moon.
Harry is trying to get information for Murphy about werewolves, so he goes to his friendly, neighborhood Spirit of Intellect (Bob is likely the equivalent of a Good or better quality Arcane Library) and asks Lore-related questions about werewolves. Between Harry's Good 3+ Lore skill, a presumably good roll of the Fudge Dice, and Taggable Aspects from having Bob as an Arcane Library resource, Harry would have gotten a rather good result, which is how/why he found out that there are a bunch of different Theriomorphs aka shapechangers, and that there are specifically four lupine-related ones.
In the case of a PC having access to a library... Unless the library was functioning as an Arcane Library, then the materials would be applicable to Scholarship, not Lore, which means that a number of potential 'bonus' Aspect tags likely would not have even applied. Further complicating that is that use of a Library (Arcane or mundane) means searching through references to find specific information. In the case of a sorcerer attempting to find out the role of the Gatekeeper... The sorcerer would first need to find out that the White Council even exists, or that it is led by a Senior Council, or that there is a member of the Senior Council who is known as the Gatekeeper. As it is, the novels still haven't stated yet whether or not the Gatekeeper is a title, or just a nickname for a particular wizard.
Now if the PC was already aware of the existence of the White Council, and stated that they were doing research on the composition of the White Council and rolled particularly well, then perhaps they could find out the names/titles of the Senior Council, or a general idea of which members fulfil what roles. For a PC wanting to know the 'inner secrets of things' that would generally indicate that the player should have a high Lore skill, and a very good Arcane library. A single roll of the dice shouldn't determine that PC always knows whatever Lore they want in any situation. If that were the case, there would be neither need or point to having the Lore skill.
So first, determine what the character is attempting to find out and assign it a difficulty appropriate to how obscure or restricted the information is. Then determine the value and relevance (or lack thereof) of any sources which are checked. Then have the player make a roll and add the character's Lore skill to the result, allowing for any relevant Aspects from an Arcane Library for re-rolls or bonuses to the roll result.
As a side note, in order for a library to be useful, there needs to be some correlation between the Resources of the library and the difficulty of the question. A character with Resources of Mediocre (0) and taking an Arcane Library at Terrible (-2) as the free Workspace is really not much better off answering Lore questions than someone with a higher Lore skill but no Arcane Library. Now when people have an Arcane Library of Resources equal to a decent Lore skill (Good or better) and/or equal to the difficulty of the question being asked, then they can really make a difference.
