This action goes in two directions, and you should always remind your players of both: first, there are things PCs know that their players don't; second, there are things players know that their PCs don't. In both cases, you confer to the knowledge with a check. Also, keep in mind that this action doesn't have to involve the skill Lore specifically—it's an action a player takes when they want to interrogate the fiction for specific information.
In the first case, the PC is either fishing for further context about the scene. It's prudent to frame such action as a success check, that way the PC comes away with something for having interrogated the fiction.
Now, if the roll had yielded success at a cost, the GM could offer to provide knowledge of what might lie inside the lair or knowledge of one of the monster's weaknesses, but not both. Similarly, if the PC rolled a poor result, the GM might only say that while Finnean has no idea what they might find in the creature's lair, he remembered reading something about the cockatrice being afraid of a particular type of bird. The point of a success check when it comes to lore is to ensure the roll doesn't lead to a dead end.
Another way to resolve consulting the lore is to hand the player the reins of the fiction. This happens in the above example with the player advantage Finnean earns when he rolls high on his success check, but you can also set the entire roll up this way.
In this example, Quacryn has already succeeded at accessing the information he needs, but what exactly that information is and to what degree it impacts the fiction is now what's at stake.
While the player doesn't explicitly declare that he's "consulting the lore," the GM gives the PC the power to narrate by asking "What do you find" once the check is successful. If the player had rolled success at a cost, the GM might give the player a choice between limitations on the usefulness of the evidence (What you find is either circumstantial or corroborating—which do you choose and what is it?), or if it's poor, then the evidence might be easily dismissed by the First Executive's racist cohort: e.g., a former non-Nim aide of his filed sexual harassment charges against him.