To enhance autonomous driving, innovative approaches have been proposed to generate simulated LiDAR data. However, these methods often face challenges in producing high-quality and controllable foreground objects. To cater to the needs of object-aware tasks in 3D perception, we introduce OLiDM, a novel framework capable of generating controllable and high-fidelity LiDAR data at both the object and scene levels. OLiDM consists of two pivotal components: the Object-Scene Progressive Generation (OPG) module and the Object Semantic Alignment (OSA) module. OPG adapts to user-specific prompts to generate desired foreground objects, which are subsequently employed as conditions in scene generation, ensuring controllable and diverse output at both the object and scene levels. This also facilitates the association of user-defined object-level annotations with the generated LiDAR scenes. Moreover, OSA aims to rectify the misalignment between foreground objects and background scenes, enhancing the overall quality of the generated objects. The broad efficacy of OLiDM is demonstrated across both unconditional and conditional LiDAR generation tasks, as well as 3D perception tasks. Specifically, on the KITTI-360 dataset, OLiDM surpasses prior state-of-the-art methods such as UltraLiDAR by 11.8 in FPD, producing data that closely mirrors real-world distributions. Additionally, in sparse-to-dense LiDAR completion, OLiDM achieves a significant improvement over LiDARGen, with a 57.47\% increase in semantic IoU. Moreover, in 3D object detection, OLiDM enhances the performance of mainstream detectors by 2.4\% in mAP and 1.9\% in NDS, underscoring its potential in advancing 3D perception models. The code will be released.