One thing I'd like to add is that Lyons himself was the one who ordered the Pitt Scourged and everything of value taken back home when he was sent on a recon mission to the place not long after the BoS arrived in D.C. Events of that magnitude can easily change a man. Not hard to imagine he had a similar revelation as Ashur did, that maybe, just maybe, the BoS should solve problems instead of just shooting them. It would also explain why he was so fond of Project Purity, all those people at the Pitt turned into mindless, horrific beasts either in body or mind from contaminated water.