Libraries are points of access to the underworld, the place where of the shades live. Go into any library and wander into the stacks, see the blank faces of those who are reading there among the moldering books. They are like the faces of the shades that greeted Odysseus in book 11 of the Odyssey, staring blankly without passion. Odysseus needed to give the shades sheep blood in order for them to speak, and when we read we are offering the ancestors our life blood so that they come alive again briefly. I think the most likely gods of the library would be Hades and his queen Persephone.
To quote Plato at the climax of the Apology when he is talking about Hades, “What would not a man give if he might converse with Orpheus and Musaeus and Hesiod and Homer? Nay, if this be true, let me die again and again. . . What infinite delight would there be in conversing with them and asking them questions!”