Envy demons a rare variety of Demon, whom have only been encountered on a handful of occasions by the Templar Order. Their nature is to seek out a host who holds a position of leadership, then possess it, assuming the host's identity and physical form after learning its secrets and desires. Afterward, it becomes next to impossible to recognize the original person from the demon, who acts as a near-perfect replica of its host, an almost foolproof impostor that no one under its covert control would dare question.
The Lord Seeker Lucius Corin makes use of a Envy demon pawn to masquerade as him and lead the Templar Order while he led the Seekers of Truth to their doom, as the Seekers wouldn't conform to the use of Red Lyrium. The Demon appeared in Val Royeaux to officially announce that the Chantry no longer held any control over the Templars and leaves after proposing an alliance to the Inquisitor
If the Templars are recruited into the Inquisition...
Should the Inquisitor take 'Lucius' up on its offer it is revealed that the entire meeting was a elaborate trap: to purge the order of the few Templars not affected by the Red Lyrium and to kill and replace the Inquisitor. Towards this end the Demon begins gathering information on the Inquisitor by sending its subordinates to their deaths against them in order to gather information on their leadership style.
Following this, the Demon drags the Inquisitor into the Fade where it attempts to further goad them in order to learn more information. It forces the Inquisitor to kill illusions of their allies as well as taunting them with images of what the Inquisition will look like under its rule. The Inquisitor is aided by a Compassion Spirit named Cole who guides him in purging his body of the Demon.
The Inquisitor and the templars who were not corrupted yet then team up to fight Envy's Red Templars while trapped in a barrier set up by the demon. After the barrier is dispelled The Inquisitor and their group confront the Envy Demon in the courtyard aided by Cole, whom partway through the battle assumed The Inquisitor's form to fight the group. Once the demon is finally dead the remaining templars are either conscripted into or made allies of the Inquisition.
Should the Inquisitor not side with the Templars, the fake Lucius Corin is instead revealed as a Demon later on in Cassandra's personal quest and after the Envy Demon flees Therinfal it can be stopped by Bull's Chargers during an operation with the assistance of Josephine or Leliana.
If the Mages are recruited into the Inquisition...
See alsoCodex entry: Envy Codex entry: Envy's Dogma