Demon of Wailing Agonies — ruling 1

If Demon of Wailing Agonies deals combat damage to a player at the same time your commander is dealt lethal damage, the triggered ability will trigger and the player will sacrifice a creature.

Demon of Wailing Agonies — ruling 2

Lieutenant abilities apply only if your commander is on the battlefield and under your control.

Demon of Wailing Agonies — ruling 3

Lieutenant abilities refer only to whether you control your commander, not any other player’s commander.

Demon of Wailing Agonies — ruling 4

If you gain control of a creature with a lieutenant ability owned by another player, that ability will check to see if you control your commander and will apply if you do. It won’t check whether its owner controls their commander.

Demon of Wailing Agonies — ruling 5

If you lose control of your commander, lieutenant abilities of creatures you control will immediately stop applying. If this causes a creature’s toughness to become less than or equal to the amount of damage marked on it, the creature will be destroyed.

Demon of Wailing Agonies — ruling 6

If a triggered ability granted by a lieutenant ability triggers, and in response to that trigger you lose control of your commander (causing the lieutenant to lose that ability), that triggered ability will still resolve.

Demon of Wailing Agonies : règles, fonctionnement et interactions (MTG)

Demon of Wailing Agonies is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Flying Lieutenant — As long as you control your commander, this creature gets +2/+2 and has "Whenever this creature deals combat damage to a player, that player sacrifices a creature of their choice."

How it works : Demon of Wailing Agonies

Original English text — Wizards of the Coast / Scryfall

#1November 7, 2014· Wizards of the Coast
If Demon of Wailing Agonies deals combat damage to a player at the same time your commander is dealt lethal damage, the triggered ability will trigger and the player will sacrifice a creature.
No other card is named in this ruling.
#2November 7, 2014· Wizards of the Coast
Lieutenant abilities apply only if your commander is on the battlefield and under your control.
No other card is named in this ruling.
#3November 7, 2014· Wizards of the Coast
Lieutenant abilities refer only to whether you control your commander, not any other player’s commander.
No other card is named in this ruling.
#4November 7, 2014· Wizards of the Coast
If you gain control of a creature with a lieutenant ability owned by another player, that ability will check to see if you control your commander and will apply if you do. It won’t check whether its owner controls their commander.
No other card is named in this ruling.
#5November 7, 2014· Wizards of the Coast
If you lose control of your commander, lieutenant abilities of creatures you control will immediately stop applying. If this causes a creature’s toughness to become less than or equal to the amount of damage marked on it, the creature will be destroyed.
No other card is named in this ruling.
#6November 7, 2014· Wizards of the Coast
If a triggered ability granted by a lieutenant ability triggers, and in response to that trigger you lose control of your commander (causing the lieutenant to lose that ability), that triggered ability will still resolve.
No other card is named in this ruling.