I only encountered lag in two areas of the game, the small transition way from Gray Road to Grass World (gladly it is short and straightforward) and the Deserted Town. I must say that navigating via the motorbike already was already painful, but using the boat was a real ordeal (even more because I didn't know where to go). the Underground map is still a big mystery for me.
I am glad to have gone as far as the lowest point of the Depths before they were modified in the newer versions.