What happens if the Bureau of Destiny tells the pattern spiders, "Things are destined to fall upwards in Nexus tomorrow?"
I suspect the pattern spiders balk. They can't and don't do that unless there's a specific reason—-a Charm or artifact or sorcery of some sort that makes stuff fall up. That's not a valid destiny, any more than "and then Chejop Kejak shows up and makes everything better for a thousand million years of peace and happiness, amen."
What happens if the Bureau of Destiny says, "Lilith gives up her quest"?
I think the pattern spiders look at Lilith's Essence pattern. If they can nudge it just a little bit, and she'll give up her quest, they do. Otherwise, the pattern spiders speaketh unto the Bureau of Destiny, lo!, saying, "I/O Error: Decision not Found."
I think the 'nudge' ability is a fixed amount—-enough to really shove mortals around, but not directly against their Nature. Exalted are progressively harder to push around.
So, the Bureau of Destiny has this mandate from somewhere: Lilith's not supposed to be on her quest. Maybe it's from self-interested Sidereals. Maybe it's from the Maidens, because Lilith is *supposed* to be hanging out with Swan-just look at her, it's in her Essence pattern and his-and this is all a horrible mess. What do they do?
They can't just tell her to give up. So they make and submit a plan that they think will recycle her shard. "Ahn-Aru and Lilith fight: Ahn-Aru wins."
This all goes swimmingly, until Lilith pulls out the whup-ass can. The pattern spiders look at the fight and at their instructions and go, "I/O Error: Outcome Not Found."
Some god somewhere sighs, and begins constructing a plan where stuff goes badly for Lilith everywhere and she gets discouraged and goes into a sulk and spends the next ten years as an owl, before Swan finds her and nurses her back to sanity.