You could even argue that a lot of slasher are revenge stories in which, although not justifiable, the killer is shown as a victim. Candyman was a victim of the racism of his time, Jason was neglected by the adults that were supposed to take care of him, Freddie was burned alive, Jigsaw was failed by a system setting him up to die, etc, etc. That is what makes them slightly more compelling characters rather than one dimensional non entities.
No... slasher movies are a pretty specific genre. The thing that defines a slasher movie is the unfairness of it; not just in the power imbalance between the heroes and villain, but in the situation. Slasher movies are about regular people in the wrong place at the wrong time getting caught up in a fight they cannot win and don't deserve to be in and trying to survive. You're usually there because the monster is cool, but your actual sympathies lie with the victims.
If that fight is told from the killer's perspective, and it's a justified one, then it's no longer a slasher movie, it's a revenge thriller.
To boil it down to its absolute fundamentals, the difference is in agency. A slasher movie is about the heroes being powerless in a situation they didn't ask for; a revenge thriller is about the hero HAVING the power and fulfilling the revenge fantasy.
My mind goes to something like The Abominable Dr. Phibes (portrayed by the late, great Vincent Price), a gothic horror revenge thriller about the eponymous Dr. Phibes getting revenge on a coalition of scientists who tried to arrange his death by subjecting them to the Ten Plagues of Egypt. By that setup it should be a slasher movie, but because they've earned their punishment and we're watching it from Phibes' perspective, each kill is a catharsis. (Also these are fun movies. It's Vincent Price in his element, campy as all hell, just a great time.)
Lily's movie COULD be a slasher movie (and probably a black comedy) if it were framed from the vampires' perspective. If we met the family, got to know them as people, and had reason to be afraid when they begin getting picked off. If the opening was the vampire patriarch maybe finding this woman shivering and cold on the road and he brings her into the house out of the goodness of his heart, but then she disappears and one of his fellows is found dead and they realize they've just released a vampire hunter into their home.
Like, it's not a terrible idea on the face of it, but Lily clearly doesn't know what a slasher movie is outside of the absolute broadest aesthetic of 'something kills lots of people'.
Also not really related but if you want a fun twist on the 'slasher movie told from the monster's perspective' I highly recommend Tucker and Dale vs. Evil.