The Vampire they are referring to is Thuringwethil, from the Silmarillion. She was (probably) a Maia who took the form of a Gigantic Vampire bat. Beren and Luthien Killed her, and then Luthien took her "shaping cloak" which she used disguise herself to get into Angbad (much as Beren used the skin of Dragluin, the Werewolf)
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