Instructions
Purchase the Black Lute from the Village Chief, who you can find in the Guild Hall. The Black Lute is available for purchase once you reach the 5-star rank. It costs 15,000z.
Fight the White Fatalis that live in the Tower area. This is the area where you must fight Elder Dragons, which is one of the quests you must take on before you'll be able to find the White Fatalis. Return to this area to fight the White Fatalis as many times as you must to get two White Fatalis Horns, one White Fatalis Webbing and two White Fatalis Scales.
Take on the Elder Quests, which you can get at the Guild Hall, to fight the Kushala Daora, a wind-elemental Elder Dragon. Keep fighting Kushala Daora until you get one Daora Jewel.
Return to the Guild Hall and speak with the Armorer. He'll give you the option to upgrade the Black Lute to the Ancient Fatalis Lied. In addition to the materials you gathered, you must pay 100,000z for the upgrade.
Unlock the Hunter Rank 9 (HR9) White Fatalis by completing the HR9 Crimson Fatalis mission and all six of the Epic Hunting Quests from the Guild Hall. These are 3-star Guild quests. Complete the HR9 White Fatalis quest as many times as you need to until you obtain two Hard White Fatalis Horns, one Strong White Fatalis Wing and two Thick White Fatalis Scales.
Fight high-ranked Chameleos, Kushala Daora and Teostra until you get three Big Elder Dragon Jewels. You'll fight these dragons when you accept G-rank hunting quests from the Guild Hall.
Return to the Armorer at the Guild Hall and speak with him again. The Ancient Fatalis Lute will now appear in the Upgrade menu. Trade the Ancient Fatalis Lied, the materials you gathered earlier and 150,000z for the Ancient Fatalis Lute.