Empires that cover, say, 1/3 or more of the game map have been known to do this ever since the map expansion to India. If that empire explodes in rebellion or civil war the sheer number of units on the map kills performance.
It is not technically possible to fix in the game as it stands, it would take a total rewrite which is not going to happen at this late stage in the game's life, I am sure. Editing the save to destroy excessive units is the only way past it.
Sorry about that!
I suspected this may be the case since lag is worse when all my vassals are involved in some kind of wars. I did not have rebellion or civil war in a while so not quite sure about that.
One thing that doesn't quite add up is that I have about 500k troops from my vassals, and raising them all at once does not seem to affect performance.