Early and accurate prediction of sepsis onset remains a major challenge in intensive care, where timely detection and subsequent intervention can significantly improve patient outcomes. While machine learning models have shown promise in this domain, their success is often limited by the amount and diversity of training data available to individual hospitals and Intensive Care Units (ICUs). Federated Learning (FL) addresses this issue by enabling collaborative model training across institutions without requiring data sharing, thus preserving patient privacy. In this work, we propose a federated, attention-enhanced Long Short-Term Memory model for sepsis onset prediction, trained on multi-centric ICU data. Unlike existing approaches that rely on fixed prediction windows, our model supports variable prediction horizons, enabling both short- and long-term forecasting in a single unified model. During analysis, we put particular emphasis on the improvements through our approach in terms of early sepsis detection, i.e., predictions with large prediction windows by conducting an in-depth temporal analysis. Our results prove that using FL does not merely improve overall prediction performance (with performance approaching that of a centralized model), but is particularly beneficial for early sepsis onset prediction. Finally, we show that our choice of employing a variable prediction window rather than a fixed window does not hurt performance significantly but reduces computational, communicational, and organizational overhead.