Event cameras and LiDARs provide complementary yet distinct data: respectively, asynchronous detections of changes in lighting versus sparse but accurate depth information at a fixed rate. To this day, few works have explored the combination of these two modalities. In this article, we propose a novel neural-network-based method for fusing event and LiDAR data in order to estimate dense depth maps. Our architecture, DELTA, exploits the concepts of self- and cross-attention to model the spatial and temporal relations within and between the event and LiDAR data. Following a thorough evaluation, we demonstrate that DELTA sets a new state of the art in the event-based depth estimation problem, and that it is able to reduce the errors up to four times for close ranges compared to the previous SOTA.