When you work for someone you are under an obligation to follow orders. Whether or not you disagree with them is not the issue. The issue is that Elder Lyons abandoned his mission without consulting with the western BOS to express his concern regarding his orders, or that he was in disagreement regarding theim.
The fact that he was successful in defeating the Enclave (with alot of help from The Lone Wanderer) would aid him in the defense of the abandonment of his mission... A mission that the Outcasts were willing to pursue, even though he wasn't.
Elder Lyons failed in both Following orders and in expressing his concerns to his superiors about his mission. So yes, he should face the Western BOS regarding the situation in DC.
BTW: I honestly can't think of one good reason why Charon would make the trek clear across the country when he's already got it pretty good in DC. Also he's just not important enough to bring back; as opposed to Elder Lyons who can help out west...Now if only he can follow orders. :whistling:
My point is that Elder Lyons, not the Western BoS, would be dictating from the position of strength.

Anyways, I doubt he'll be heading west as Bethesda will likely want him and Sarah to remain on the East Coast for sequel potential.
You're also treading some dangerous moral territory with the "orders must always be followed" argument, but this isn't the thread to discuss that, I suppose. Regardless, I don't see Lyons running back to answer to a beaten West Coast BoS that has more or less abandoned him when he's now one of the dominant powers on the US East Coast.
Charon sure would have good reason; if someone heading West buys his contract, he's bound to go. He appears to have no significant ties to the D.C. area, unlike most of the FO3 characters, and is one of the most competent fighters, meaning he'd stand one of the best chances of making it out of the FO3 cast. Most other FO3 characters either aren't believably tough enough to make it or have no reason to leave (most humans).
Fawkes is the other one who would be believable, as it's quite conceivable he would learn of intelligent Super Mutants on the West Coast and go to seek out others of his kind. He's also easily enough of a BAMF to survive the journey. Now that I think of it, he would make a
lot of sense; the West Coast is where he can finally find a group of people more or less like him.
Personally, though? I want Butch to show up, if someone has to. Tunnel Snakes rule!
I thought you were an Outcast supporter. :unsure2:
To be honest? It's pretty much impossible for me not to love any branch of the Brotherhood.

Outcasts are my favorite, but I still love the Lyons Brotherhood and the West Coast BoS.