Arthur Maxson's father Jonathan Maxson might have been the one sent East for safety.
Apparently his mother sent him east to protect him from internal conflicts in the west.
Where is Lyon's he giving away tech? He gives away water but is quick to secure the purifier himself.
Or Casdin knew Elder Lyon' wouldn't go to war over it. Fighting Casdin doesn't help Elder Lyon', and losing most or all of his men in a coup wouldn't help Casdin.
In the west vet brotherhood troops die and get replaced by nothing, as it takes two decades to breed and train a replcement. Wasteland bumpkins can be trained into killing machines ten times faster then you could breed them up naturally. Elder Lyon's was a small detatchment sent to DC with whatever technology the western BoS could afford to lose.(probably due to the last expedition east vanishing.) However to say he has crap tech is wrong in the end as he ends up with a rather sizable cache of Enclave technology making his tech actually superior to what they have out west. The image I get from New Vegas is the brotherhood in the west is dying. Veronica is rather convinced there doomed and even McNamara admits she's probably right that they'll die out if they don't change there ways.
He wouldn't and I don't see the NCR marching an army across six or seven states to reach DC either. Perhaps in another 150 years the NCR will do battle with the New Republic of Columbia. Or they would simply unite into one nation.
(D.C=District of Columbia)