Jared Wilson does a nice job of unpacking Lewis' view of the Logres:
The gist of the Logres idea is that God’s original plan for the races, nations, and peoples—and the lands they inhabit—is still here, mostly obscured and hidden, but occasionally bubbling up to the surface, with promise of one day subsuming the ruins with their truer selves. In these literary works, characters captured by a better vision—the vision of Logres—operate according to the true England, the truer and better sense of their place.
Doubling off of that, in That Hideous Strength Lewis navigates the distinctiveness of national identities and the relativity of them all in light of Christianity:
"There's no special privilege for England--no nonsense about a chosen nation. We speak about Logres because it is our haunting, the one we know about...
If one is thinking simply of goodness in the abstract, one soon reaches the fatal idea of something standardised--some common kind of life to which all nations ought to progress.
Of course, there are universal rules to which all goodness must conform. But that's only the grammar of virtue. It's not there that the sap is. He doesn't make two blades of grass the same: how much less two saints, two nations, two angels.
The whole work of healing Tellus depends on nursing that little spark, on incarnating that ghost, which is still alive in every real people, and different in each. When Logres really dominates Britain, when the goddess Reason, the divine clearness, is really enthroned in France, when the order of Heaven is really followed in China--why, then it will be spring."
On the weekend where we celebrate our nations independence from the Logres, it's worth reflecting about the distinctiveness of our country and that, as someone wise once said, when we meet God we just might do so as Americans.