Although existing 3D perception algorithms have demonstrated significant improvements in performance, their deployment on edge devices continues to encounter critical challenges due to substantial runtime latency. We propose a new benchmark tailored for online evaluation by considering runtime latency. Based on the benchmark, we build a Latency-Aware 3D Streaming Perception (LASP) framework that addresses the latency issue through two primary components: 1) latency-aware history integration, which extends query propagation into a continuous process, ensuring the integration of historical feature regardless of varying latency; 2) latency-aware predictive detection, a module that compensates the detection results with the predicted trajectory and the posterior accessed latency. By incorporating the latency-aware mechanism, our method shows generalization across various latency levels, achieving an online performance that closely aligns with 80\% of its offline evaluation on the Jetson AGX Orin without any acceleration techniques.