I’ve never heard of vigilante justice against someone already sentenced to prison for life, just because they were sentenced in a place without capital punishment?
(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…)
It's probably rather difficult and risky to enact vigilante justice against someone who's in prison.
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.