Aren't Lyon's bunch of metal-coated, mutant-slaying, Enclave-wooping, BoS chapter the real outcasts? They are no longer sent supplies by the central Brotherhood organisation, as well as setting their own objectives, over what the Codex says? Shouldn't it be them wearing the black and red armour? Post your thoughts...

Yes. Technically they are the "outcasts" and the "Outcasts" are the actual BOS. Or they represent them anyway.

I'd say almost but not quite. The BoS outcasts are only called that as Lyon's coined the term or something. So the outcasts are outcasts of rejects.

Technically even though they do keep to the codex where Lyons group doesn't, they're still not members of the Brotherhood anymore because Lyons had their names removed from the records after the schism. Lyons group is still considered to be part of the Brotherhood by the elders back west, they just don't get anything in the way of support from them.

This.