I misremembered about Maxson, but your wrong about not making sense on a retreat. You would do precisely that if you were trying to withdraw essential personnel before being completely crushed by a force with superior numbers. We aren't talking about a retreat designed to regroup into a more favourable position, as you are, we are talking about a retreat designed solely to preserve the existence of your "race". The last desperate stand to allow "civilians" to escape is actually pretty common in media (there are some examples, nothing too recent but that has more to do with advanced weapons tech killing you no matter where you go). Regardless the point is moot, as you said he was sent after the expedition East.
Though I have still yet to see any evidence from you about why it doesn't make sense that holds water. A lot of your complaint that it doesn't make sense seems to stem solely from your belief that the BoS does not need to be in every Fallout. Oddly enough though, despite your assertion that the NCR is more important to Fallout, only a single faction has actually been present in every fallout game ever made, and as far as I'm aware in all of the cancelled FO games (Van Buren, Tactics 2, Extreme, BoS 2).
I guess that does put it in perspective, I didn't realize just how recently Lyons was cut off. It also makes the actual time-line of the NCR v WCBoS war a little more interesting to me.
Anyway, back on to topic:
I honestly would prefer it to be the members of the BoS from tactics that didn't crash with the MWBoS near Chicago. Actually I kind of wish they had gone with that explanation for the CWBoS.