If Deathless Knight enters your graveyard after you've gained life in a turn, its last ability can't trigger during that turn.

Deathless Knight must be in your graveyard immediately after you gain life for its last ability to trigger. If you gain life due to damage from a source with lifelink, and that damage is dealt at the same time that lethal damage is dealt to Deathless Knight, it won't be in your graveyard until state-based actions are performed a moment later, and so the ability can't trigger.