In short, a transition from one type of lung to the other is not possible, because no "transitional" lung could function properly.
This is a common misunderstanding. We think of organisms as being like machines with parts that either work or don't. Parts are either properly designed and working or they aren't. To understand evolution, we need to step away from these kinds of assumptions. These assumptions are projections; they assume that a particular form
ought to have a specific function. Science is not prescriptive, it is descriptive. In real world biology, there is no progression or purposeful drive towards some finished, perfect, properly functioning product. This kind of progression requires foresight, and this kind of metaphysical foresight has no place in science.
All biology cares about is "does this attribute increase the chance of the organism surviving and producing offspring and is this attribute heritable?" If the answer is yes and continues to be yes over a period of time, whatever that attribute is will tend to increase in the population. As far as evolution is concerned, if the attribute confers a survival advantage, it is functioning "properly." It doesn't have to be full and complete according to some human evaluation of the attribute to confer that advantage.