So let me get this straight: the two highest figures of Hell have their agendas filled with 100% wholesome content, while the angel participates to all the dirty deeds by her own volition?
Is there a chance that at some point in the future, Azazel's halo just floats away from her head and lands on Judgement's, to everyone's confusion?

Did her short stint as a furry icon make Lucifer fall in love with all things cute and fluffy? Certainly an amazing thing to bridge the gap between two bitter individuals.

Luci and Judgment having outright animosity toward each other, moreso than Judgment just ignoring her authority is interesting to know. Need some more of that DEEP LORE.

If I had to guess though… I think it could be in reference to the original idea of Hell being Lucifer's prison, and not his kingdom. So possibly at some point, HT Luci was a prisoner herself and ended up taking over as the CEO Queen, and Judgment's pretty miffed about it, as it's clear how zealous she is about her job. As great as the slice-of-life stuff is, a prequel comic would be interesting see.