The Dutch Ghost said:
Emil wanted them to be the shiny heroes in army, protecting the wasteland downtrodden from the evil Super Mutants and Enclave, bringing water to the thirsty, and that is what Bethesda did.
I had a bit of a different take. The whole thing about protecting humanity from the super mutants was self-gratifying propaganda. They went around spitting on the 'locals' constantly. They weren't so much protecting the locals as killing super mutants because the super muties represented a threat. The capitol brotherhood didn't have the bunkers they could hole up in. They had a fortress at the pentagon, but it was a very visible and very large, and ultimately vulnerable structure. Lyons was smart enough to know that a static defense never works in the long run. (something the west coast bos hasn't learned yet) So they had to start going out and killing the super mutants to keep the population under control.
Killing super mutants also saves the "locals" like Three Dog, so Three Dog plays them up as heroes, but nothing they did in F3 was really heroic or selfless. Before the enclave showed up, all they did was go around keeping the super mutant population low enough that it wouldn't overwhelm them. But even this slight lifting of the siege mentality caused a bunch of brothers to go awol.
Once the enclave showed up, they still didn't much care until they got their hands on massive water purification technology. Now thats something that the Brotherhood just can't abide. However, once they have it, what do they do with it? It's pumping clean water into the potomac, they can't keep it a secret. They can't move it. So what does Lyons do? He uses the propaganda three dog had laid out and gets the rest of the wasteland essentially working for him, distributing the water. (If he hadn't he'd be overwhelmed with refugees) Additionally, Liberty Prime lets them easily annihilate Enclave, so he goes after the Enclave and their tech.
I'll grant you, Lyons is much more flexible and innovative than the brotherhood normally is, but if you look at what he
does rather than what he
says (and what's said on his behalf), what you see really isn't all that far from brotherhood thinking, given how much more difficult his circumstances are.