This work addresses the challenge of adapting dynamic deadline requirements for LiDAR object detection deep neural networks (DNNs). The computing latency of object detection is critically important to ensure safe and efficient navigation. However, state-of-the-art LiDAR object detection DNNs often exhibit significant latency, hindering their real-time performance on resource-constrained edge platforms. Therefore, a tradeoff between detection accuracy and latency should be dynamically managed at runtime to achieve optimum results. In this paper, we introduce VALO (Versatile Anytime algorithm for LiDAR Object detection), a novel data-centric approach that enables anytime computing of 3D LiDAR object detection DNNs. VALO employs a deadline-aware scheduler to selectively process input regions, making execution time and accuracy tradeoffs without architectural modifications. Additionally, it leverages efficient forecasting of past detection results to mitigate possible loss of accuracy due to partial processing of input. Finally, it utilizes a novel input reduction technique within its detection heads to significantly accelerate execution without sacrificing accuracy. We implement VALO on state-of-the-art 3D LiDAR object detection networks, namely CenterPoint and VoxelNext, and demonstrate its dynamic adaptability to a wide range of time constraints while achieving higher accuracy than the prior state-of-the-art. Code is available athttps://github.com/CSL-KU/VALO}{github.com/CSL-KU/VALO.