This paper introduces a prognostic method called FLASH that addresses the problem of joint modeling of longitudinal data and censored durations when a large number of both longitudinal and time-independent features are available. In the literature, standard joint models are either of the shared random effect or joint latent class type. Combining ideas from both worlds and using appropriate regularization techniques, we define a new model with the ability to automatically identify significant prognostic longitudinal features in a high-dimensional context, which is of increasing importance in many areas such as personalized medicine or churn prediction. We develop an estimation methodology based on the expectation-maximization algorithm and provide an efficient implementation. The statistical performance of the method is demonstrated both in extensive Monte Carlo simulation studies and on publicly available medical datasets. Our method significantly outperforms the state-of-the-art joint models in terms of C-index in a so-called "real-time" prediction setting, with a computational speed that is orders of magnitude faster than competing methods. In addition, our model automatically identifies significant features that are relevant from a practical point of view, making it interpretable, which is of the greatest importance for a prognostic algorithm in healthcare.Read less <