You're all assuming Lyons and NCR would even come to blows. Being that the Eastern BoS is far more concerned with keeping the general peace and helping settlements stay standing, Lyons could very well see the NCR as much-needed reinforcements.

Remember, Lyons isn't Maxson or McNamara, he actually knows the value of and respects his neighbors.

Far more likely would be Casdin starting something stupid and ending up a corpse.

I believe Casdin is already corpse in a few years,outcasts will never rejoin BOS and hence wither they will grow old and die or just have to eventually leave DC...