Lieutenant abilities apply only if your commander is on the battlefield and under your control.
07-11-2014
wotc
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.
07-11-2014
wotc
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.
07-11-2014
wotc
Lieutenant abilities refer only to whether you control your commander, not any other player's commander.
07-11-2014
wotc
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.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.