Dying raises the average age if you die below the average age, and lowers the average age if you die above the average age. Thus, a 16-year-old dying can only lower the average age if the average age was already less than 16. A four-month-old dying can only lower the average age if the average age was already less than 4 months. (Which, obviously, it can't be.)

Dying lowers life expectancy regardless of when you do it, and it has a stronger lowering effect the earlier you do it. The dying four-month-old has a really strong negative effect on life expectancy, but a strong "positive" effect on the average age. They're orthogonal[1] concerns.

[1] OK, not technically orthogonal. One will help predict the other, especially if you know the average age. But the point remains that a negative effect on life expectancy can be associated with any effect at all on the average age, because all effects of death on life expectancy are negative.