Real-time X-ray tomography pipelines, such as implemented by RECAST3D, compute and visualize tomographic reconstructions in milliseconds, and enable the observation of dynamic experiments in synchrotron beamlines and laboratory scanners. For extending real-time reconstruction by image processing and analysis components, Deep Neural Networks (DNNs) are a promising technology, due to their strong performance and much faster run-times compared to conventional algorithms. DNNs may prevent experiment repetition by simplifying real-time steering and optimization of the ongoing experiment. The main challenge of integrating DNNs into real-time tomography pipelines, however, is that they need to learn their task from representative data before the start of the experiment. In scientific environments, such training data may not exist, and other uncertain and variable factors, such as the set-up configuration, reconstruction parameters, or user interaction, cannot easily be anticipated beforehand, either. To overcome these problems, we developed just-in-time learning, an online DNN training strategy that takes advantage of the spatio-temporal continuity of consecutive reconstructions in the tomographic pipeline. This allows training and deploying comparatively small DNNs during the experiment. We provide software implementations, and study the feasibility and challenges of the approach by training the self-supervised Noise2Inverse denoising task with X-ray data replayed from real-world dynamic experiments.