Minimally invasive interventions often rely on live 2D X-rays for image guidance. Yet, anatomical localization and procedural accuracy can be enhanced by spatial alignment of these intraoperative X-rays with 3D preoperative computed tomographies (CTs). This 3D/2D registration problem is typically formulated as pose estimation of the X-ray source relatively to the CT, which is done by simulating synthetic X-rays from 2D projections of CT volumes. However, the optimization-based refinement used by the state-of-the-art deep learning approach takes several seconds, thus exceeding the allowed time budget in live image guidance. In this paper, we propose LXPose (Live X-ray Pose estimation), a self-supervised multi-stage 3D/2D registration framework for real-time image guidance. LXpose removes the dependency on optimization and leverages a two-stage CNN trained with a projection loss to ensure high accuracy and computational efficiency. Moreover, we apply extensive data augmentation to mitigate the domain gap between simulated and real X-rays. Overall, LXPose yields comparable 2D registration error to the state-of-the-art method, while reducing inference time to 20 ms, which demonstrates the potential of LXPose for real-time clinical deployment. Our code is available at https://github.com/fedefacente/LXPose.git .