Season 3: One change and the story ends uneventfully
Here's the spoiler: had First Chair and Second Chair brought the Grey Books out of the storage facility for the kidnappers to view, then the point of episodes 5 and 6, and part of 4, vanishes. That's how safe deposit boxes and closed stack libraries and special collections all work: you request an item, your qualifications are checked, and if you are allowed, they bring the specific box or book to you in a little room. Jeezes petes.
Have MI5 check what is in the boxes before the kidnappers look at the files and poof, the plot vanishes even faster.
Or is the point of the episode that First and Second Chair are oblivious to a simple solution? And Lamb doesn't suggest it because he "can't be arsed."