From what I understand, Omniarch is a statement of status rather than a concept of its own, and as such tends to lack style and identity (similarly to Omnipotence, whose many flavored expressions are usually a lot more interesting).
I generally have a hard time wrapping my head around conceptual powers, as they are inherently disconnected from reality and all the grounding references that come with it, which are necessary components to make sense of a character, its abilities and journey.
In the case of Conceptual Lordship, I imagine it would be best to start off with the manipulation of a specific concept the character vibes with, and gradually expand his abilities to neighboring concepts while also increasing his mastery of them, and slowly transitioning from manipulation to physiology, eventually culminating with Conceptual Lordship as we know it.
With powers like this one that essentially grant you everything on a silver plate, it is the process/journey to get there that would logically make the backbone of the story, as once you reach its full-power and everything becomes achievable with the merest thought, there isn't much left to write about.