Lifetime update will pass the destruction of the unit to side counting system, resulting in a "unit lost" condition.
Deletion update is more direct and just removes it from the game without any further notice.
At least that's my impression from doing tests with both...
I don't know. Probably either SUICIDED or just plain NORMAL. Best way to find out is to have a distinguishable death animation for some of the DeathTypes. Whichever animation plays when it dies is the one that's triggered by LifetimeUpdate's DeathType.