When Deathwing briefly relocated to Draenor in the aftermath of the Second War, the great black dragon built a new lair on a rocky island a short flight east of Hellfire Peninsula and the Skeletal Coast. It served as the headquarters of Deathwing and the other dragons allied with the Horde during the Dark Portal Crisis after the Second War. However, Deathwing made a tactical error in capturing Kurdran and Sky'ree, as this brought the wrath of Archmage Khadgar and Alleria Windrunner upon him. The pair freed Kurdran, who proceeded to raze the Lair to the ground.
Deathwing was originally reported killed in the battle, but in fact had returned to Azeroth. He left behind a clutch of eggs in his lair, which later hatched as Nether Drakes transformed by the energy released during the dustruction of Draenor. This implies that the lair still exists, however, it is not found in World of Warcraft.
Deathwing's Lair (Azeroth)
Deathwing also had a lair on Azeroth, but little is known about it or its location. But it could be at top of Mount Hyjal in the Onyxia-alike cave.
Map of the Hellfire and Skeletal regions of Draenor, including Deathwing's Lair