Respiratory diseases are one of the most common causes of death, and their early detection is crucial for prompt treatment. X-ray dark-field radiography (XDFR) is a promising tool to image objects with unresolved micro-structures such as lungs. Using Talbot-Lau XDFR, we imaged inflated porcine lungs together with Polymethylmethacrylat (PMMA) microspheres (in air) of diameter sizes between 20 and 500 μmμm200μm0.57μm20cm over an autocorrelation range of 0.8–5.2 μmμm200μm0.57μm20cm. The results indicate that the dark-field extinction coefficient of porcine lungs is similar to that of densely-packed PMMA spheres with diameter of μmμm200μm0.57μm20cm, which is approximately the mean alveolar structure size. We evaluated that, in our case, the autocorrelation length would have to be limited to μmμm200μm0.57μm20cm in order to image μmμm200μm0.57μm20cm-thick lung tissue without critical visibility reduction (signal saturation). We identify the autocorrelation length to be the critical parameter of an interferometer that allows to avoid signal saturation in clinical lung dark-field imaging.