(I mean - people get killed in prison sometimes, I suppose, but it’s not really like vigilante justice on the streets is causing a breakdown in society in Australia, say…)
I think the problem is with places where they don't have life sentences at all, but rather let murderers back out into society after some time. I don't know if vigilante justice is a problem there in reality, but at least I can see it as a possibility: someone might still be angry that you murdered their relative after 20 years and come kill you when you're released.
Having recently done an in-depth review of arguments for and against the death penalty,[1] I can say that this argument is not prominent in the discourse.
Sometimes, suspects don't even make it to the jail.
https://en.wikipedia.org/wiki/Jack_Ruby_Shoots_Lee_Harvey_Os...
https://en.wikipedia.org/wiki/Tulsa_race_massacre
Uncommon or not, vigilantism is incompatible with justice on a societal level, regardless of any alleged guilt of offenders.
Without a showing of evidence, a trial of the accused, and a verdict that withstands judgment, we're left with theories and conjecture, and hatchets long left unburied.