Before you can establish how Ulorian society works, you have to establish how Ulorian society works. Standing national armies are a very recent invention among humans. There's every opportunity to get very creative.
We needn't flatten Ulori attitudes the way Tolkien did: we're not trying to replication Roman Catholic theology, and Lorgalis isn't a stand-in for Satan's bestie. Indeed, Lorgalis is a unique personage in Kulthea, and a society under his control should be similarly unique, reflecting him.
He would, of course, stand over all. But the strong do not rule the weak simply because they're strong. They rule because they offer the weak protection, and not only from themselves. Lorgalis is one of the most accomplished spell casters since the First Age, and such heights are only achieved if they grow out of an academic tradition -- they also give rise to them.
We see that other Elven societies are organized around Houses, it's not unlikely to see something of the like in Ulor -- though Dyari are more strict in their hierarchical orderings than Loari or Linaeri.
Thus, at the top is the House of Lorgalis, which directly controls the Dyari Great Houses of Ulor. Those houses jockey for position with regard to one another, perhaps harboring the hope of being able to challenge Lorgalis someday. Lorgalis would be aware of this and plot to keep any of them from growing too powerful, even as he needs to keep them strong enough to maintain his realm against that which attacks from outside or beneath.
Does it start to become clear why Lorgalis finds it so easy to manipulate the politics of Jaiman? He's scarcely unpracticed at this.
The Great Houses establish position through the individual power of it's members, replicating the fundamtal Dyari dynamic: The strong protect the weak in exchange for service. They have a thousand ways of determining who is more powerful, and by how much, and a dozen words translated as "spouse" by those who don't know to distinguish between "senior spouse through mutual voluntary contract," "senior spouse through personal conflict," "junior spouse by concession from one House to another" etc. A House is made up of Clans, and Clans of Families, each replicating the power structure on smaller and smaller scales until we are looking at individual Dyari.
Each Dyar seeks to maximize their power, as expressed by their personal ability and the resources they control. This Dyari Magician establishes a College where others may practice their Art. That Dyari warrior secures the loyalty of a platoon of Qaidu or Lugrok - or perhaps tames and rides a Wyvern. These cadres all come together when needed - by order of the Head of the Clan, or even Lorgalis himself, to accomplish a military goal.