You can unlock this quest as early as Haven however it will take a long time to fully complete depending on how quickly you proceed through the Inquisitor's Path Quest's. All you need to do is find 12 primeval red lyrium deposits and destroy them in order to complete the mission.
Red Lyrium Deposit Access/Location Chart:
|Storm Coast||4||1) Unlocked Storm Coast|
2) Varric's Personal Quest Lines Completed (Any Inquisitor's Path Quests having to do with Hawke)
3) Started/Completed "Red Water" Side Quest
4) Completed the War Room Operation "Red Templars on the Storm Coast" (Power Cost 4)
5) Once you travel to the location unlocked by "Red Templars on the Storm Coast" you will have access to the area where the 4 Red Lyrium Deposits are. CAUTION: You may need to slay a dragon so go prepared and all enemies will be level 18 or higher.
|The Hinterlands||3||1st Deposit - At Fort Conner in central Hinterlands. You will need to defeat Templars|
2nd Deposit - Begin the "Stone Dreams" side quest which is activated by reading a note inside and abandoned home just north of the Crossroads. You'll find a cave, there will be a minor battle with a mage, and you can explore the cave to find the Lyrium deposit.
3rd Deposit - Near an Inquisition campsite in the North-Eastern part of the Hinterlands where there is a dragon nest. You can attempt to destroy it without battling the dragon but it will be VERY hard to do as there will be constant fireballs from the sky as it swoops around. There will also be Dragonlings attacking you as soon as you enter the area.
|The Western Approach||3||1st Deposit - Sand Rock Mine. You will need at least one mage in your party so they can energize the blocked entrance and clear debris.|
2nd Deposit - Forgotten Mine
3rd Deposit - Shimmer Stone Mine
|The Emerald Graves||3||1st Deposit - Veridium Mine|
2nd Deposit - Left Side of the Villa Maurel
3rd Deposit - Located in the Northern area of the Emeral Graves in Southfinger Watch.
|Emprise Du Lion||5||Should be rather easy to access across the countryside/caves. Probably easiest place to gather deposits, just make sure you're level 15 or higher.|
GAMER TIP: Luckily there are well more than 12 red lyrium deposits located throughout the game so if for some reason you find yourself unable to get to some you may be able to find more somewhere else. Make sure to bring Varric along if you want to earn more approval with him. Before you finish the quest you will earn slight approval if he is not present and great approval if he is present. After you hit your 12 deposit limit for the quest you will not gain any additional approval with Varric unless he is in your party.