In this article, a compressive sensing-based reconstruction algorithm is applied to data acquired from a nodding multibeam Lidar system following a Lissajous-like trajectory. Multibeam Lidar systems provide 3D depth information of the environment, but the vertical resolution of these devices may be insufficient in many applications. To mitigate this issue, the Lidar can be nodded to obtain higher vertical resolution at the cost of increased scan time. Using Lissajous-like nodding trajectories allows for the trade-off between scan time and horizontal and vertical resolutions through the choice of scan parameters. These patterns also naturally subsample the imaged area. In this article, a compressive sensing-based reconstruction algorithm is applied to the data collected during a relatively fast and therefore low-resolution Lissajous-like scan. Experiments and simulations show the feasibility of this method and compare the reconstructions to those made using simple nearest-neighbor interpolation.