Lyons and his BoS come off as nice guys. If they come across a peaceful faction that has no intrest in joining or even helping the BoS. Would they use force against a peaceful faction?
Very interesting idea. Based on how they came off as during FO3 I'd say they wouldn't. :/
If this story were to expand I guess they'd have to meet a "not nice" faction or the leadership of this Capital State would have to be much more aggressive by the time they met the rival.
If anything I'd assume the primary rival would have to be the Outcasts. I'll just reiterate my theory from before:
Maybe the Outcasts would be forced out by the State or just leave, and ultimately reach the Commonwealth and the Institute. Grow in strength by taking advantage of the hi-tech stuff there, return, and present a serious, and a very Brotherhood-of-Steely threat to the Capital State.