Time-resolved imaging of the thorax or abdominal area is affected by respiratory motion. Nowadays, one-dimensional respiratory surrogates are used to estimate the current state of the lung during its cycle, but with rather poor results. This paper presents a framework to predict the 3D lung motion based on a patient-specific finite element model of respiratory mechanics estimated from two CT images at end of inspiration (EI) and end of expiration (EE). We first segment the lung, thorax and sub-diaphragm organs automatically using a machine-learning algorithm. Then, a biomechanical model of the lung, thorax and sub-diaphragm is employed to compute the 3D respiratory motion. Our model is driven by thoracic pressures, estimated automatically from the EE and EI images using a trust-region approach. Finally, lung motion is predicted by modulating the thoracic pressures. The effectiveness of our approach is evaluated by predicting lung deformation during exhale on five DIR-Lab datasets. Several personalization strategies are tested, showing that an average error of 3.88 +/- 1.54 mm in predicted landmark positions can be achieved. Since our approach is generative, it may constitute a 3D surrogate information for more accurate medical image reconstruction and patient respiratory analysis.