In That Which Remains Us, Faramir inherits a set of keys:
"[The chest] was locked, of course, but Faramir fished about in a pocket and drew forth a set of keys that he had taken from the desk. One of them clearly was meant to open a room somewhere in the Citadel--possibly the high chamber where once the palantír had sat--and a second had opened a small box that had proved to hold letters exchanged between Rohan and Gondor in the past five years. Thus, the third must be for the trunk. Faramir inserted it into the keyhole and gave a twist. Nothing. The key did not budge, and would not, despite a few well-chosen words and several further attempts."
This is my attempt to answer the question: what does the third key in the set open?
Thinking of the key, each confirms a prison
Given a choice in the matter, Denethor would not have had them in the city together. But the summons had already gone out to Ithilien when a grey dawn had brought with it the wizard Mithrandir, begging leave to visit the vaults of the library. Both had now departed yet again, but not before their old alliance had been reformed. Neither would be drawn on what they had discussed - and, as a consequence - the Steward of Gondor now found himself surveying his younger son's room.
The bookshelves had revealed little beyond an inexplicable taste for the Arnorian Visionaries, and a more reputable one for History. Some of the annotations in these volumes had proven distracting, and thus it was well past noon before Denethor had at last turned his attention to the desk. A plain, rather than a handsome affair, this stood beneath the long windows on the south-facing wall, where it would catch the sunlight. Denethor sat down in the chair and looked over the desk with few expectations. It had plainly been tidied before its owner's departure. A sheaf of paper lay neatly at the far left-hand corner, beneath a weight. Denethor picked this up, recognizing at once the blue and white splinters of glass and the dolphin motif. He set it down again with a frown. The only other item on the desk was a slim blue book of verse, well-thumbed and well-read. He did not examine this.
The desk drawers themselves yielded disappointingly little. Two were given over entirely to letters, but these turned out to be from family, bound neatly according to correspondent. The third contained a stack of music. And the fourth, as expected, was locked.
He laid a worn leather pouch on the desk and took from within four metal keys. They had a milky patina from long years hidden from use. The third he tried unlocked the drawer.
The books inside were of many shapes and sizes and the eldest lay at the back. He lifted out this hoard and selected the first, a small green leather daybook.
I take up my pen to begin this journal on the day when my brother begins his great adventures.
Denethor looked to the top of the page to see the date. Boromir's sixteenth birthday, the day he was confirmed in his lieutenancy. Faramir would have been… ten? eleven?
He turned the pages slowly, scouring the writing. Leaf by leaf, volume by volume, the words slipped by.
Wasted day. Council knows how it stands in Ith. & I tire even myself repeating it. Yet shd. - it seems - be grateful to be granted the time in which to speak...!
Enough. You become too alike! You leave again soon. Until then - restraint, as ever, becomes you.
Six months had passed since that entry, and only a page or two were blank at the end of the book. There was no other in the drawer, nor that he could see around the room. There is naught here, he thought, and noted with mild irritation how low the sun now stood in the sky. Naught of use. Whatever had passed between his son and the wizard - if indeed his son had kept a record - would be in the current journal and that, no doubt, travelled with him. The matter would have to wait until it too joined the rest.
He sat up at the desk, and set the book back in its place at the top of the pile. Then, almost on a whim, he took out the first and read again the opening entries. At least his style has improved, he thought absently. And his script. Then he locked the drawer, and added the key to the set.