I think this would depend on their cultural norms, and not ours. In a world where life and death always worked this way, culture would have evolved in vastly ways than in ours. So I think there is no point in regarding this question as if it were set on Earth in the 21st century where the laws of the universe suddenly changed into this. I think you'd have to build up their cultural norms from prehistoric times to modern times and determine that way what makes sense for them.
In the beginning, I guess there would have been much more religious significance to death, for example, killing would be ritualistic and only allowed for the religious class or the ruling class. But even before that, (maybe before developing consciousness, even) I think parents would have killed some of their own offspring if they weren't able to feed them or if they were born deformed. In wars, the warriors would not have taken slaves, killing would have been the endgame. By the way, what happens if a woman dies in childbirth? Does that count as the baby having killed the mother?
But even if killing would be much more common and possibly there would not be the same taboo attached to it as in human society, they would have had to consider leaving enough people alive to grow food and such otherwise they would have died out. And maybe due to this cult to killing the population is not as numerous as on Earth. Maybe people do not form as close groups as today, certainly there would be no cities because living in a place where no one would notice if a person goes missing is not exactly a life insurance.
The question is: would your beings ever develop democracy if certain members of it already have such a great advantage to newborn ones? I don't think so. So it is likely that the execution would be done by someone of the ruling class or someone of the priest class. Maybe they would determine the winner of the privilege based on merit or maybe they would hold a lottery.
If you want them to regard life (especially "newborn" people's life) as precious as we do, you'd have to find a reason to declare killing people a sin because I don't think they would have any scruples about killing. They would regard it as a boon and as such, in a society where human life is a diminishing resource, only the most powerful would gain it.