Respiratory-induced organ motion is a technical challenge to medical imaging, nuclear imaging, and radiation therapy for lung cancer treatment in particular. In our previous works, we have developed a lung tumor tracking approach based on a patient-specific finite element model of the respiratory system, which takes into account the physiology of the respiratory motion and the non-reproducibility of these movements. The lungs deformations are determined by ribs kinematics together with diaphragm motion. The lung model is monitored and controlled by two measurable parameters: ribs kinematics and lungs volume changes. Over all phases of respiration, the model is able to predict the lung tumor motion with high accuracy. Despite the benefits offered by these models, they are limited by their time-consuming computations, which makes difficult their use in a clinical routine. In this paper, we propose to use a hybrid approach combining a biomechanical patient-specific simulation of the respiratory system and machine learning methods to predict, in real-time, the lung tumor position during Radiation Therapy (RT). We have evaluated and compared two deep learning models trained and tested on lung tumor trajectories datasets created from our patient-specific biomechanical simulations of the respiratory system.