From what I know of SHARK's campaign, raising the dead is impossible, and paladins are the authorities. Those two points shape the argument substantially.
Well, not really. Julia's dead and the vampire suffered a minor inconvenience. That's pretty clearly a loss for the forces of Good, whether she can be raised or not.
As for the tiefling, I wouldn't question the paladin one bit if he had hanged her on capture or after a suitable enquiry. That would be a lawful act and a deserved punishment for the evil things she had (presumably) done in Archerrus' service.
In the circumstances the killing was not an act of justice properly given, but a case of the guy with the sword either killing the nearest thing because he felt the need to kill something, or taking vengeance on another uninvolved creature for the vampire's killing of Julia. I call that chaotic evil.