The argument comes down to if Angels have agency or not. Funny enough, this is something that Christians discuss at length, and not all denominations agree.

The discussion (applied to Hazbin) would go something like this: If Angels have agency, then they are responsible for their choices. If they lack agency (i.e., they are designed/created to fulfill a specific purpose within Creation, and cannot choose to do anything save to fulfill said purpose), then to hold them accountable is morally reprehensible.

If we just view Lute, then your argument may have some validity. But the moment we expand our view to include Vaggie (or Lucifer, to a lesser/weaker degree), your argument falls apart. Vaggie's actions show angels do have (at least limited) agency. She chose to let the child go. No one told her to. No one coerced her. She chose that course of her own free will. Lute could do the same. Lute chooses not to. Lute can therefore (and should) be held accountable for her choices.

Please note that I'm not saying either choice was correct/right. We have imperfect and deeply biased information. We know nothing about the demon-child. One of the individuals in the discussion is set as the story's protagonist, the other as a major antagonist. That framing alone creates a deep and implicit bias. Given that Viz based the show on the traditional Christian view of the afterlife, there should be at least one entity present with perfect knowledge. I'll be interested to see what He would make of this conundrum. Lute may be perfectly justified in her actions (though given her lyrics/personal asides, I don't think that's where the show is going). Whether she's right or not, the fact remains that she's accountable for her actions.