The problem is surface area versus volume. Also called the square cube law.
Lungs require surface area to gather oxygen. They do this by making thin walls in the lungs where blood is on one side and oxygen on the other, giving oxygen a chance to get bound to the red bloodcells. Whenever you double the size of the creature a rough estimate gives you 4x more surface area in the lungs. Despite lungs being 3D the actual place where the oxygen passes into the blood is still a 2D surface. The body uses ingenious methods to increase that surface area but its about at its limit.
The rest of the creature is made up out of cells. Each extra cell requires extra oxygen to live. These cells occupy a volume. If you double the size of a creature it roughly receives 8x more cells to feed oxygen to.
So with each time you double its size, you need to make the lungs 4x as big to still give the body the same amount of oxygen to live as its not-doubled counterpart.
In other words, by the time you reach Kaiju size you need a whole lot more than 1 extra lung, you are going to need several dozen extra lungs. But don't worry, your Kaiju will also create more heat and only have the surface area of its skin to lose it effectively, so it might overheat and die before it can suffocate!
As for whales: they swim (relatively) slowly and use a lot of tricks to reduce their oxygen use when they dive for long periods of time. But if you were to make them move and fight as much as a Kaiju would their oxygen use would go through the roof again.