Object detection and global localization play a crucial role in robotics, spanning across a great spectrum of applications from autonomous cars to multi-layered 3D Scene Graphs for semantic scene understanding. This article proposes BOX3D, a novel multi-modal and lightweight scheme for localizing objects of interest by fusing the information from RGB camera and 3D LiDAR. BOX3D is structured around a three-layered architecture, building up from the local perception of the incoming sequential sensor data to the global perception refinement that covers for outliers and the general consistency of each object's observation. More specifically, the first layer handles the low-level fusion of camera and LiDAR data for initial 3D bounding box extraction. The second layer converts each LiDAR's scan 3D bounding boxes to the world coordinate frame and applies a spatial pairing and merging mechanism to maintain the uniqueness of objects observed from different viewpoints. Finally, BOX3D integrates the third layer that supervises the consistency of the results on the global map iteratively, using a point-to-voxel comparison for identifying all points in the global map that belong to the object. Benchmarking results of the proposed novel architecture are showcased in multiple experimental trials on public state-of-the-art large-scale dataset of urban environments.