When the token copy of Vaultborn Tyrant enters the battlefield, its second ability will trigger.

If Vaultborn Tyrant was copying something else when it was last on the battlefield but somehow still had its last ability, then the token enters the battlefield as whatever Vaultborn Tyrant copied, with the listed exceptions.

If one or more static abilities that apply to a creature entering the battlefield change its power, those abilities are considered when determining whether or not Vaultborn Tyrant’s second ability triggers. The same is true for replacement effects that apply to it, such as entering the battlefield with one or more +1/+1 counters or entering the battlefield as a copy of another creature.

Except for the listed exception, the token copies exactly what is printed on Vaultborn Tyrant and nothing else (unless Vaultborn Tyrant was copying something else; see below). It doesn’t copy whether Vaultborn Tyrant was tapped or untapped, whether it had any counters on it or Auras and Equipment attached to it, or any non-copy effects that changed its power, toughness, types, color, and so on.

Once Vaultborn Tyrant’s second ability has triggered, lowering the power of the creature or removing it from the battlefield won’t stop you from gaining life and drawing a card.