Pulmonary lobe segmentation in computed tomography scans is essential for regional assessment of pulmonary diseases. Recent works based on convolution neural networks have achieved good performance for this task. However, they are still limited in capturing structured relationships due to the nature of convolution. The shape of the pulmonary lobes affect each other and their borders relate to the appearance of other structures, such as vessels, airways, and the pleural wall. We argue that such structural relationships play a critical role in the accurate delineation of pulmonary lobes when the lungs are affected by diseases such as COVID-19 or COPD. In this paper, we propose a relational approach (RTSU-Net) that leverages structured relationships by introducing a novel non-local neural network module. The proposed module learns both visual and geometric relationships among all convolution features to produce self-attention weights. With a limited amount of training data available from COVID- 19 subjects, we initially train and validate RTSU-Net on a cohort of 5000 subjects from the COPDGene study (4000 for training and 1000 for evaluation). Using models pre-trained on COPDGene, we apply transfer learning to retrain and evaluate RTSU-Net on 470 COVID-19 suspects (370 for retraining and 100 for evaluation). Experimental results show that RTSU-Net outperforms three baselines and performs robustly on cases with severe lung infection due to COVID-19.