I made that assumption because lungs aren’t really inside, they are pretty close to the surface, so they are easy to expand. If they were inside, they would have to push other organs away.
And regarding increasing the overall volume of the body, I addressed that in another comment. Basically, Godzilla would have to visibly swell by a lot, to have that much buoyancy.
It could be that the swelling is only in the underwater part, but then Godzilla would tip over with any slight movement, because the center of mass would be way above water.