I could see many within Lyons group saying to themselves "now that the people have their clean water, we can finally get back to our original mission." So they finally tell Lyons to shove it and join the Outcast. So Lyons is only left with a handful of original Brotherhood and noobs that they recruited.
I can't see Lyons guys trying to force Megaton or Rivet City into their group or under their protection. I don't think Lyons ever had that as his goals. With much of the BoS leaving to join the Outcast, groups like Rivet City might try to take Project Purity for themselves.
Those that finally do join the outcast could make off with alot of the captured Enclave tech and totally screw Lyons over. Kinda turns the tables, the Outcast then try to get Arthur Maxson back. So a civil war in the wasteland.
Would be kinda funny if the Outcast end up destroying Project Purity. They take it apart and make off with the high-tech parts.
I think it'd be interesting if a handful of people decided to join the Outcasts post-F3 and this finally caused Sarah to crack.
In fury she leads Lyons' Pride to attack the Outcasts and they end up driving them from their bases to the northern CW. War starts between Lyons and the Outcasts.
Lyons is furious with Sarah for disobeying direct orders and she is dishonorably discharged from the Brotherhood. She wanders out into the wasteland and is never seen again.
The war rages for a few years before Lyons is assassinated by an Outcast agent who disguised as a wasteland and got himself recruited.
The Outcasts demand that the Brotherhood hand over Arthur Maxson but Rothchild takes command and the CWBoS (which had been falling apart without a leader) unites once more.
Rothchild is a more deceptive and desires power over charity.
He uses his men to stage themselves as a raider gang and increase activity near Megaton to convince them to make Springvale a CWBoS base. When Vault 101 opens they all become known as three districts to one settlement.
He annexes Rivet City easily, all he uses is some propoganda and offers them benefits.
He takes over Cantebury Commons and Bigtown with ease, they were weakening because of the war with the Outcasts.
He then invades Tenpenny Tower and makes a large settlement around it.
With all of these settlements on his side Rothchild has the man power to push the Outcasts from the CW completely. He then begins to form a country (the Capital Union).
The Outcasts decide to go investigate this Institute they've been hearing so much about and they head north.
When they get there the Institute is in pretty bad shape. More and more androids are becoming self awair and leaving which is causing an extreme lack of security for the scientists (most, if not all, of secuirty would be made up of androids). The Outcasts offer an alliance, they protect the scientists in exchange for advanced technology, particularly weapons and androids.
They agree and the Institute is fortified, the Outcasts feel as though they're keeping technology in the right hands and feel like they can live out their existance like this.
Then they hear of the CWBoS becoming a nation and expanding north. They begin to fear that someday their old enemies would reach them so they begin to make deals with settlements throughout the Commonwealth (such as take out a raider gang for the settlements being harassed by them to join them) and they became known as the Federation of the Commonwealth.
The FC expanded south as the CU expanded north and eventually the two met in Philidelphia (going off of WONDERWOMBAT's ideas perhaps the Pitt can also be there to have a three side faction war which would ironically be made up of people who were all part of the Brotherhood expedition to DC).
This would make for a very interesting game.