Bogsnes: Really, I am not sure if it is even possible to win it and I am the goddamn DM. Anyway, let's skip the Iron Siege discussion.
PhaedrusXY and the rest of the lot: Here is a brief history of Nine Hells leaders. Hopefully I get it all right.
When the Overlord of Hell (whose avatars both Asmodeus and Lucifer are) was separated from the other paragons of law (together they were called the Trinity), he crashed in the Depths Below and his monstrous body created all the nine Perditions, Lake of Fire and Brimstone presenting one of his veins. In due time first creatures emerged from the blood of the Overlord and sought to impose their rule on others.
Millenia passed before the Overlord woke and found himself in a weakened state. He decided to create an avatar, Lucifer the Satan, who flew through Hell and told everyone to either submit or be destroyed. Eight most powerful of the malefircareim, the hellspawn, were given a layer. These were Astaroth, Dispater, Mammon, Adrammalek, Leviathan, Lilith, Sammael and Mephistopheles and they, along with the Satan, formed the original Lords of the Nine.
Then came the Dawn of the Gods. First deities emerged, angels were spawned and so forth. Soon all the gods made a combined effort and trapped all fiends of Duke of Hell status and higher to their own home realms and Lucifer started his personal war against the Realms Above. This war grew so large that it threatened the existence of Hell and Overlord needed another plan. He would show to the world that evil can be won and Lucifer destroyed. This is why Asmodeus came to Hell and started plotting against the Satan.
Beherit and Astaroth joined forces with Asmodeus and to a great surprise the Battles of Light and Greed ended is Asmodeus' triumph and the Satan was either exiled or destroyed, no-one knows. Asmodeus destroyed Beherit and cast Astaroth out of Hell and changed his name to Garhauth who now is a demigod in Abeir-Toril, he was replaced by the new Lady of the First, Tiamat.
Millions of years passed and the Great Fall occured. Thousands upon thousands of angels were cast to Hell and soon they started gaining more and more powerful positions. Beelzebub and his network of spies slowly trapped the absent-minded Poison of Perdition, Sammael to his fortress and soon he fled to the Gray Wastes of Despair and so the first fallen had reached Lordship. The new Lord of the Seventh, Archduke of Maladomini, Beelzebub also immediately started his war against Mephistopheles.
With the help of Beelzebub Belial encountered Adrammalek and with Asmodeus' silent consent he was crowned as the new Lord of the Fourth. At around this time Geryon betrayed Leviathan and gained the Lordship of the Fifth Perdition and Beelzebub urged his servant Moloch to take his armies to Lilith's realm, Malbolge.
Some more millenia passed and Moloch had taken over Malbolge, because Lilith concentrated too much on the Mortal Coil. Asmodeus declared Moloch to be the new Lord of the Sixth and he immediately started abusing the former Lady of the Fifth, a habit that would last until the end of Dies Irae.
At this point the classic Lords, Mammon, Dispater and Mephistopheles were scared for their thrones and for a good reason. Tiamat gave up her Lordship voluntarily in favour of yet another fallen, Astarte. Now it was four fallen angels against three devils true and the son of Aesmadeva (the very first pit fiend) and Tiamat, Geryon.
Eventually small battles became full-scale wars and Asmodeus decided something was to be done. He told Geryon Dies Irae was going to occur and started preparing himself for a war. How right he was, the skirmishes between Mephistopheles and Beelzebub grew and in retaliation Astarte marched his armies to the infinite iron fields of Dis; the civil war had started. This infamous war ended in a huge battle at the bottom of Malsheem, Asmodeus fortress, and when the Lords were battling, Geryon blew his horn... Asmodeus appeared and stripped all the Lords of their powers and send an army of pit fiends to subdue them.
In due time all Lords were down and the pit fiends who eventually won them would become the very first Dark Ministers who run the Blood War. Asmodeus gave everyone a chance to submit, except for Geryon who was stripped of his Lordship for good in favour of Leviathan, but Lilith had poisoned the mind of Moloch who spat at Asmodeus' face and in response he was cast out of Hell. Lilith and Leviathan had gained their Lordships back. This even also destroyed the alliance between Mammon, Dispater and Mephistopheles as the Lord of Avarice used the civil war as a chance to steal enormous amount of wealth from the Lords of the Second and Eight.
Millions of years later a pit fiend general called Bael overthrew Astaroth and Glasya started ruling with Mammon, but was soon moved to Dis. This is the formation we have now.