Exit Edron Castle from the south and follow the path east toward Stonehome. When you cross the bridge exiting Edron, go north along the mountain until you find Avar Tar. Go up the ramp west of Avar Tar to reach the mountain pass of the Edron Wyvern Hill.
Follow the mountain pass west all the way and go down at the end of it. Do not go up as this is the Edron Wyvern Hill.
Go north until you run into a large hill. Turn west and continue until you find another hill (here). This is the Edron Dragon Lair. You may encounter a Wyvern on the way here. Orshabaal spawns on the way too, but you shouldn't encounter him.
Go down the ramp inside the mountain. You will encounter 2 Dragons here. Go north and down the hole.
Nothing is here, just go north and rope up to get to the main area.
You're now in the main area of Edron's dragon lair. Go north and be prepared to face many Dragon Hatchlings and Dragons. On the middle of the floor there is a ramp going down. Go down it when you find it.
Down the ramp you'll find a single Dragon Lord. Kill it and go down the hole.
To the west is a level 60 Gate of Expertise and nothing else. Go through the gate and down the hole.
Immediately you will find 3 Dragon Lords and 3 Dragon Lord Hatchlings. Kill them all and claim the first rewards in the chest on the south-west corner of the room. You will find a Ring of Healing, Dragon Necklace and 7 Small Diamonds. If they haven't been taken yet, you may also find another chest with 300 Gold Coins, a Steel Shield, Plate Legs, a Double Axe, a Dark Helmet and a half-decayed human Skeleton.
In order to obtain the Fire Axe you must find the pick hole on this floor. It is 2 sqm south-west of where you came from, or 3 sqm east and 5 sqm north of the quest chest (see also the image below). You may need to use Destroy Field Runes here. When you have picked open the hole, go down and use the Pile of Bones to obtain the final reward, the Fire Axe.