I don't think that sense of "of" applies. "Platos and Xenocrates'" is a compound plural noun that stands for something like "examplar" or "prominent/great intellectuals". Second, the Lyceum of Athens is referred to as a place in both instances:
I shall suppose myself in the Lyceum of Athens
The second mention of the Lyceum is indirect:
that famous seat of philosophy
The "of" preceding the second reference to the Lyceum indicates "origin", like "the people of Russia". Citizens are not instances of the general category of country, but constitute a country or reside in the country. So the sense of "of" being used is closer to indicating an association between two entities, typically one of belonging. Here the entites are "Platos and Xenocrates'" and "The Lyceum of Athens".
A more straightforward, tounge-in-cheek rendering may be something like this:
I suppose myself on the floor of the US Senate, repeating the lessons of my masters before the Harry Reids and Mitch McConnells of that famous seat of politics as my judges, and in presence of the whole human species as my audience.
Ok, so perhaps less dramatic, but it shows using more familiar objects that the "famous seat" referrs to the physical location and the two "examplars" belong or are associated with that location. At least that's my read of it.