I can't find a good link, but I think that the average is dragged down significantly by infant death and that a life expectancy of 40 doesn't mean that you should expect to die at 40 if you've already made it to adulthood.
This is a fable. Many people reached old age in the empire and even the middle ages. A low "Life expectancy" doesnt mean people didnt grow old. It just means that many people die prematurely of (now) preventable things.
Death of the mother in childbirth ( 1 in 10)
Death as a child because of unsafe surroundings
Death as a child because of childlabour
Death because of infectious wounds
Death because of plagues and sickness
Death because of random violence
Death because of war
Death by famine
Death by accidents like fire in the house, occupational hazzard or hunting. Or the sinking of a ship.
All these things lower Life expectancy. But with luck and a good physique many of them could be avoided.
It's closer to a misleading truth or a fallacy. Life expectancy really was that low, but it was driven by child mortality, so knowing the mean life expectancy doesn't give an accurate picture of life expectancy upon joining the army in one's late teens.