Yes. Lizardmen are like aliens, most people don't even know they exist. Ontop of that, Lizardmen sincerely don't care about the other races enough to ever band together with any of them. They're cold, calculating yet bestial.
Vampires on the other hand have more in common with the mortals, that's why the Vampire Counts sided with the Empire against Chaos (though Vlad went double-traitor by later joining Nagash, one of the evil Tomb King characters). They did that because no matter what, the vampires still need the living and don't want to serve Chaos. Apart from the Blood Knights that turned to Khorne, cus blood.
Saltzpyre already tolerates Sienna (a renegade witch) and Kerillian (a wood elf with her own gods counter to Sigmar, and she can also become a Shade as a spec which means Khaine worship), so I don't think a vampire would be too much of a stretch. That said, a vampire might also be too cool
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Not during the End Times. Emperor Karl Franz made Vlad von Carstein an Elector Count for his aid in defending Altdorf.
I think they could make it work if they wanted to. Or maybe we could get a Bretonnian, that would definitely work without any trouble!
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No Greenskins present to fight the Empire during the End Times. They're elsewhere, stompin' stunties and the entire eastern empires by themselves.
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I think this might be very much it, sadly. Instead, they will add new specializations for the current characters.