Whenever Enbringer Umbra (or other effects like shudderwock repeating her battlecry) triggers Blightblood Berserker it has lifesteal. But the lifesteal is tied to the original Berserker, not the deathrattle.
When you trigger the deathrattle of a card that is not on the battlefield, I believe the game uses the base version of that card as the source of the deathrattle.