he success of supervised LiDAR perception methods relies on the availability of large sets of labeled point cloud data, for which the labeling process is costly and time consuming. Given unpaired LiDAR datasets of similar sizes from two domains, with one (source) containing task-specific labels e.g. 3D bounding boxes for all frames, but only a small percentage of frames being labeled in the other (target) domain, it is challenging to train a model that generalizes well on validation data from the target domain. In this paper we propose a novel LiDAR few-shot domain adaptation architecture and training strategy to address this challenge. Our method is based on adapting a task-specific network (3D object detector) to work within the CycleGAN framework modified to operate with LiDAR features, and on the joint end-to-end training of generators, discriminators, and task-specific layers. To overcome nonconvergence issues we propose a training strategy that introduces a mechanism to delay the joint learning between the generators/discriminators and the task-specific network by allowing them to start learning independently, while slowly introducing joint learning as they converge, hence avoiding instability during the early stages of the training. Our proposed integrated architecture enables a direct way to evaluate the performance of the model instead of feeding pre-computed generated data into a separate pretrained model. We include an experimental section where we evaluate our proposed architecture on the publicly available KITTI and Nuscenes datasets, as well as on our own labeled dataset. We present useful mean average precision plots that illustrate the benefits of our domain adaptation architecture as a function of number of labeled target domain frames.