>>18991496It is a teleporter puzzle, you need to get through the teleporters and over the right one way jumps until you get to the stairs to the roof, once you get to the roof you can fight him.
As for Lugia, Whirl Islands, once you know where he is you can get there quickly (don't have to travel very far if you pick the right entrance). Iirc you can do it after Pryce because you only need Whirlpool if you take a certain route, but you might need waterfall, I forget. I know the easiest route requires Waterfall.