Future founders of the Outcasts were merely dissatisfied with Lyons' focus on protecting the wastes by killing super mutants, seeing it as an ineffectual waste of men and resources that would ultimately destroy the Brotherhood.
The group did not plan on separating originally. Their secondary objective was to keep dangerous technologies out of the hands of raiders, tribals, and everyone else without the aptitude necessary to safely utilize them. The Outcasts attributed their departure to their belief that Elder Lyons had lost sight of the Brotherhood's true mission, and the reason for their presence in the Capital Wasteland the discovery and acquisition of advanced pre-War technology. The Brotherhood Outcasts were a contingent of Brotherhood of Steel soldiers who split from Elder Lyons' group at the Citadel in 2276.
5 Interactions with the player character.