What the west coast Brotherhood needs to do is attack Lyons and take his version down while they still can like the Outcasts seem to want to do.
Lyon's goals are alot easier to swallow and his standards are obviously lower, so I imagine it would be pretty easy for his idea of the BOS to expand further.
Basically, the real BOS need to put him down before he changes the face of the BOS altogether and turns a vital search for the last glowing embers of humanity into a neverending slap fight/pissing contest with a bunch of supermutants. Lyons is destroying more tech than saving it.
The problem is that between them lies Midwestern BOS who are not pleased with the west coast fraction, then we have NCR which are standing in their way, Casears Legion, several former members of Masters Army expanded into that direction, radioactive dust storms, raiders etc etc.
So even if they wanted to take the tech from Lyons Brotherhood they'd lose a lot of men trying to wander across a continent.
It's not very realistic and they have their own problems to deal with.
If Circle Of Steel is canon then they have another problem on their hands.