In order to predict in real-time the lung tumor position during Radiation Therapy (RT), we have developed a new hybrid approach combining a biomechanical patient-specific simulation of the respiratory system with machine learning methods using neural network LSTM (Long Short Term Memory) model. Our LSTM model is entirely built and trained on simulated data from our patient-specific biomechanical simulations of the respiratory system. To explore the LSTM performance, we have generated a few representative lung tumor trajectories by simulating different types of breathing patterns. We have evaluated our approach on real patient data, from the public DIRLab data set. Over all phases of respiration, the results show that our approach is able to predict the lung tumor position within an average time of 0.05 second at high accuracy and a mean-square error (MSE) less than $1 mm$. These results constitute a preliminary step towards a real-time non-invasive lung tumor tracking approach during radiation treatment.