The time period referenced is ambiguous, but the OP said to assume the best possible conditions for each faction. for Lyon's BoS, that means having liberty prime operational. This can also be interpreted as the in-game ending that leads to each particular faction having the most power (i.e. best game ending circumstances), in which case, Fallout 3's broken steel add-on leaves us with the destruction of Liberty Prime.

I'm not sure which assumption was intended to be made, but I completely agree that if the Eastern Brotherhood doesn't have Liberty Prime, the NCR would destroy their chapter in a heartbeat.

Post limit.