I think it makes more sense to think in terms of the canon version, if only because Maxson is too young to be the Lone Wanderer by a good ten years or so, though there are other reasons besides that.
My take on it is:
Maxson's hero figures as a child were Sarah Lyons and the Lone Wanderer, two figures with extensive combat experience and a preference for military solutions to problems, and Elder Lyons who he respected as a leader when he was a child but later viewed as misguided.
Sarah Lyons died in combat, probably before Elder Lyons died, while fighting super mutants to defend the Capital Wasteland. The Lone Wanderer did as their name implies and wandered away to carry on their adventures in the wastes, pursuing whatever whims and drives motivated them after the death of their father. Elder Lyons died with no clear successor and was succeeded by a series of ineffective leaders with little skill at command who frittered the Brotherhood away trying to pursue Lyon's goals.
So his soldier hero died a martyr, his outsider hero left after his duty was done proving the merit of wastelanders to him, though also their unreliability, and his peaceful childhood leader died and had his legacy disgraced by those who came after him. Maxson winds up spending a lot of his youth as a soldier under the command of ineffective leaders with no military experience and few concrete goals.
Being part of the military branch of the Brotherhood, as well as having had a great deal of respect for soldiers in his childhood and having been taught the Maxson line was one of strong leadership and tradition he comes to the conclusion that the Brotherhood needs military leadership, a strong hand at the helm and to reshape itself without the isolationism of the West Coast Brotherhood or the soft hand of Lyons' Brotherhood. Absorbing the Outcasts contributes to the new perspective of the Brotherhood as it takes on some of their animosity to outsiders.
This leads to the new East Coast Brotherhood, highly militant, authoritarian, interventionist, short on mercy, more than a little paranoid, with more authority granted to the military branch over the scientific and administrative branches. Maxson expands recruitment to keep numbers up as he steps up their operation to kill all feral ghouls and mutants in the Capital Wasteland, and sends out scouts to look for threats and possible resources in nearby areas, which leads to the invasion of the Commonwealth.