Your “Vampire Lord” will only be Special Summoned by his own effect when destroyed and sent to the Graveyard by a card effect that your opponent controls, not by your own card effects or as a result of battle.
“Vampire Lord” will only return to play with his effect when the owner controls it, because “Vampire Lord” must be “destroyed and sent to YOUR Graveyard”. When your opponent takes control of your “Vampire Lord”, and it inflicts Battle Damage to your Life Points, then the first effect of “Vampire Lord” is activated. But the second effect will not be activated if “Vampire Lord” is destroyed and sent to the Graveyard while your opponent controls him.
If you Summon “Vampire Lord” and he is destroyed by your opponent’s “Horn of Heaven” or “Solemn Judgment”, “Vampire Lord” will be Special Summoned in your next Standby Phase.
When “Vampire Lord” is destroyed (by a card effect such as “Chain Destruction”) while in your hand, in your Deck, or on the field, he will be Special Summoned in your next Standby Phase. If “Vampire Lord” is discarded from your hand it will NOT be Special Summoned.
When “Vampire Lord” is Tributed (including by your opponent with “Soul Exchange”), or when he is “sent to the Graveyard”, he will not be Special Summoned by his own effect because he was not “destroyed”.
If “Vampire Lord” is supposed to be Special Summoned, but your Standby Phase is skipped with “Solomon’s Lawbook” or “Gamble”, “Vampire Lord” won’t be Special Summoned, not even on the following Standby Phase.
If “Vampire Lord” is supposed to be Special Summoned, but gets returned to your hand or Deck instead, he won’t be Special Summoned.
If “Vampire Lord” is destroyed and sent to the Graveyard by your opponent’s card effect, but returns to the field that same turn and is then destroyed in a manner that would not allow him to be Special Summoned, then he is not Special Summoned.
You can keep Special Summoning “Vampire Lord” as long as each time he is destroyed by your opponent’s card effect.
“Vampire Lord” is Special Summoned to your side of the field; you cannot Special Summon him to your opponent’s side of the field.
When you have your “Vampire Lord” in play, Special Summoned by your “Premature Burial” or “Call of the Haunted”, and your opponent destroys “Premature Burial” or “Call of the Haunted” with “Mystical Space Typhoon”, the “Vampire Lord” won’t be Special Summoned because it was destroyed by your card effect, not by your opponent’s. If your opponent controls your “Vampire Lord” with “Autonomous Action Unit”, and “Autonomous Action Unit” is destroyed, “Vampire Lord” won’t be Special Summoned because the owner did not control him.
When you Special Summon “Vampire Lord” with his effect, your opponent can negate the Special Summon with “Royal Oppression”, but the “Vampire Lord” will have been destroyed by your opponent’s card effect (“Royal Oppression”) and will be Special Summoned again during your next Standby Phase.
If “Vampire Lord” is destroyed while equipped to “Relinquished”, he won’t be Special Summoned, no matter who controls him or who destroyed him.
If “Vampire Lord” is destroyed while face-down by “Sasuke Samurai”, “Vampire Lord” will be Special Summoned by his effect.
“Vampire Lord” can be Special Summoned by his own effect even while “Necrovalley” is in play.
When “Vampire Lord” is Summoned while your opponent’s “Rivalry of Warlords” is active and your only monsters are non-Zombie-Type monsters, “Vampire Lord” is destroyed, but is not considered destroyed by “Rivalry of Warlords”’ effect and won’t be Special Summoned.
When your opponent doesn’t have the type of card that you declared for “Vampire Lord”, the effect of “Vampire Lord” disappears but you get to look at your opponent’s Deck to confirm it.
It is the controller of “Vampire Lord”, not necessarily the owner, that names a card type.
When you name “Spell Card” for “Vampire Lord”, it includes Normal, Quick-Play, Field, Ritual, Continuous, and Equip Spell Cards, and the same is true for Traps.
Card effects like “Penguin Knight”, “Sword of Deep-Seated”, and “Cockroach Knight” will activate their effects when sent to the Graveyard by “Vampire Lord”’s effect.
Netrep Rulings:
“Vampire Lord” will only be Special Summoned through its effect if it is destroyed by the opponent’s card effect while under the control of the owner.
If the opponent, after taking Battle Damage from “Vampire Lord”, does not have the type of card declared in his or her deck, a new type of card may not be declared.
If “Solemn Judgment” is activated in response to the summon of “Vampire Lord,” that “Vampire Lord” will be Special Summoned through its effect at the player’s next Standby Phase because “Vampire Lord” was destroyed.
If “Vampire Lord” is equipped to “Thousand Eyes Restrict” and destroyed, it will not be Special Summoned through its effect because it was not a monster card when it was destroyed.