It depends. Homicide rates in contemporary hunter-gatherer societies are significantly higher than in large-scale formal societies. That may be due to the lack of formal law enforcement (i.e. the general weakness of informal modes of dispute resolution), or it may be a function of the general marginalization of hunter-gatherer peoples in today's world. Or both.

But that aside, _average_ life expectancy probably didn't start to rise significantly until after the invention of sanitation and antibiotics, since viruses and bacteria have always been the biggest killers.