Well, thanks for warning us that your argument is going to be fallacious.
Context matters. Lynching has a long history, and the very fact that you chose that manner of murder (and used it on a black person, no less) suggests that you're aware of your connection with that history. So "for the lulz" is no longer an adequate characterization of the criminal's motives.
(I also still think that social power dynamics are relevant to the categorization of hate crime: if a serial killer targeted exclusively left-handed victims, or unibrowed victims, I probably wouldn't consider it a hate crime because "sinistrophobia" isn't a thing in our society. Now, if people started making a trend of targeting left-handers, at some point I'd have to reconsider and ask myself what's causing the pattern. At some point, the pattern itself, regardless of cause, becomes a societal problem that makes life more difficult for left-handers in general. Which is generally the reason we treat hate crime specially.)
wrt litcrit: your loss, but if you ever change your mind, we can discuss it over discounted grande skim lattes sans foam.