I've done this assault about 30 times so far.
First thing that is confirmed (not by me personally) is that the Divisor Ring drops from this Assault. Or at least is supposed to. (like I said, I've done this about 30 times so far).
General strategy is this:
We usually go in with RDM/WHM, THF/NIN, BLU/NIN. Yes, 3 jobs. That's it.
RDM buffs everyone, then we talk to the NPC to get the first set of buffs/debuffs. There are 4 different sets of buffs/debuffs and they don't stack (once you get a new buff/debuff the old one wears.) These buffs are as follows:
Attack +, Slow +
Accuracy +, Attack -
Movement Speed +, HP -
Healing MP +, MP -
There may be a 5th buff/debuff combo, but those are the ones I remember offhand.
Anyway, back to the strategy. Once you have a buff/debuff applied (by talking to the NPC), one of four sets of lamia will spawn. These are in set spawn points, and they are as follows:
1) Down a passage to the northeast, off a ledge (pull them back up)
2) Down a passage/staircase to the south
3) Around an ice floe to the west through a tunnel
4) South of the ice floe to the west through the same tunnel as #3.
So once you have the buff applied, find which lamia group spawned and start fighting. They link by sight so you want to pull artfully. Thief's "Hide" ability works too so if you get a link, hide and pull one out of the pack.
There will always be a BLM in each group of lamia, whose spells are interrupted quite easily by BLU's "headbutt" spell. There can also be a RNG or COR (won't roll dice) as well. Maximum lamia in a group is 3.
Once a group is defeated, talk to the NPC to spawn a new set of lamia and apply a new buff/debuff group. Once you do this four times the crate will appear and the assault is won.
Possible "good" drops are ??? footwear -> Ataractic Solea and ??? ring -> Divisor Ring.