Once inside pick up a Lugian Pick Axe off the ground near the Lugian Miners. You will need this to collect ore blocking your path.
Make your way through the mine as far South as you can go, and use the Surface Portal. Which will drop you into the Ancient Lugian Fortress. (see map for route)
Bring the Well-Balanced Lugian Greataxe back to the Mine Chamberlain in the Withered Atoll Lugian Mine for your rewards.
Notes
There is a Lugian Lifestone in the fortress that can be tied to.
You will also find Rusty Lugian Axes in the fortress, pick up as many as you like and turn them in to the Sanamar Collector on any character for 15,000 xp and 10,000 pyreals each!
Axe may only be turned in once, everyone completing this quest will need their own.