One thing I am curious about is how the Qm is going to handle Lu tens death
I'm a little confused by your use of "going" here, largely because it implies
Arsonist's Lullaby hasn't
already handled Lu Ten's death and instead suggests this is something it may, or should, do in the future.
This confuses me because at the end of the previous loop (the second-most recent update), Azula tore into Iroh verbally, focusing specifically on attacking him over the siege of Ba Sing Se and Lu Ten's death, throwing that death directly in his face as a weapon—it was, in fact, explicitly the raw emotion in this diatribe that led to Iroh reevaluating his opinion on Azula in a way that left him open to the more seismic shift in his opinion that her subsequent conversation with Zuko provoked.
Afterwards, at the start of the current loop (the most recent update), almost the entirety of its wordcount revolves around Lu Ten's death, including a scene where Azula visits his room and—in a rare moment for her—engages in some fairly deep introspection about his death as a lens through which to evaluate her own life. Furthermore, as part of that, she specifically and explicitly considers the implications Lu Ten's death had on the succession.
I'm… not sure how much more I can handle it than that?
(Ironically, in a (pretty awful) unpublished draft of the idea that after many revisions eventually became this one, I have even written that (very different) version of Azula actually using "Ozai was responsible for Lu Ten's death" to goad Iroh over what she perceives as his failures to stop Ozai from destroying their family one by one—but even there, her next paragraph of internal monologue is about how she's lying when she says it and Ozai was only responsible for Ursa and Zuko.)