mental health" seemed like an attempt to make out he was some kind of victim of something, even though everything that happened were his own life choices
That's what made Kim snap. He was pretending to his patrons he was having some kind of mental breakdown*.... When really he was pissed because his wife had caught him cheating and given him an ultimatum.
Someone who was having a genuine breakdown/depression/suicidal ideation was being further triggered by Evan's tweets, believing him to be suffering in the same way.
When Kim tried to ask Lloyd to be careful what he posted in case it pushed this young man over the edge, Lloyd reacted in a self centred, petulant way. Unable to see for once it wasn't just about him. Ranting about his "rights" to tweet.
*(He used the the catch all term "mental health". Like the controversial word 'woman' when something means everything, it ends up meaning nothing.)