Chamber of the dragon mosaic
The small round chamber is a juncture which lies at the bottom of a shaft where half a dozen tunnels meet. On the floor is a scuffed mosaic of the three-headed dragon of House Targaryen done in tiles of black and red.
To one side there is an ornate iron brazier fashioned in the shape of a dragon's head. It is kept lit to warm the chamber; there is a sullen orange glow given off by the coals in the beast's yawning mouth. Each door leading to the chamber is closed off by an iron gate.
A Clash of Kings
Varys delivers Shae to Tyrion Lannister’s bedchamber in the Tower of the Hand. Tyrion, who is surprised to see her, asks her how she entered the room. She tells him that Varys made her wear a hood as he escorted her but there was one place where she got a peep at the floor and saw a picture in tiles of a dragon, in red and black. The dragon was past an iron gate that Varys had to unlock with a key. 
A Storm of Swords
Locked in the black cells beneath the Red Keep, Tyrion is rescued by his brother, Jaime Lannister. After Jaime confesses the truth about Tysha, Tyrion abandons him and finds Varys, who leads him deeper, down to the fourth level where King Maegor had built torture chambers.
When Tyrion and Varys enter a small round chamber Tyrion sees the mosaic of a three-headed dragon wrought in red and black tiles. He realizes that it is the place that Shae told him of. He states to Varys that they are below the Tower of the Hand, which Varys confirms. Tyrion realises that the series of rungs set in the wall will take him to what is now his father's Tywin Lannister's bedchamber. Tyrion climbs up the two hundred and thirty rungs, confronts his father and slays him.
A Feast for Crows
During his search for Tyrion in the Red Keep's tunnels Jaime finds himself in a chamber at the bottom of a shaft where six tunnels meet. He sees the mosaic of the three-headed dragon and it seems to Jaime as if the beast addresses him in Prince Rhaegar Targaryen’s voice:
|“||I know you, Kingslayer, the beast seemed to be saying. I have been here all the time, waiting for you to come to me. And it seemed to Jaime that he knew that voice, the iron tones that had once belonged to Rhaegar, Prince of Dragonstone. ||”|
As he stands vigil over his father Tywin’s corpse, Jaime finds himself recalling the mosaic and the time when he said farewell to Prince Rhaegar in the yard of the Red Keep during Robert's Rebellion, and the words they exchanged, before the Prince of Dragonstone rode forth to his doom in the Battle of the Trident.
A Dance with Dragons
In the cabin of a ship fleeing across the narrow sea Tyrion does not remember waddling through the darkness with Varys at his side after killing Tywin. He must have clambered back down the shaft, two hundred and thirty rungs to where orange embers were aglow in the mouth of an iron dragon.