In the United States, we have specialists who treat lung conditions called respiratory therapists. My mother was one in the 1990's and she said it was very difficult to convince many elderly patients with asthma to quit smoking since they had been told by their doctors in their youth it improved their asthma. She dealt with hundreds of patients with lung conditions, most who would have been young in the 1920's-1940's. I think this is pretty good proof that this odd medical advice was indeed given.
Smoking causes the airways to constrict, so it can reduce some symptoms of asthma such as wheezing, even though the person is less able to breathe, so it is bad for them and can cause a lethal asthma attack. Quitting smoking also temporarily causes coughing fits as the airways open up, so you can see why these people were skeptical. I imagine this is how such wrong-headed medical advice became orthodox.
People thought it was so good for the lungs, you can see the cyclists in the Tour de France smoking along the way in now iconic photos from the era.