The Outcasts are here for the reasons explained above, and it's a reasonable estimate to say it'd be around a decade after. The series is rather centeral in it's time frame. And they kept the name for the proud bearings of the originals. The outcasts called themselves such and were never afraid to say it's what they were hence why it was kept.

I never said Lyons was out here, the BoS are everywhere and again it was explained in the Outcasts description why the fight was here as well. Neither of the leaders are the same, these are completely separate chapters torn by internal conflict. It's was to be explained in the story itself how the NCR got so far east and for the sake of that I won't explain it here because this entire system to to let people learn from the wastes. If they want to know, their characters will ask.