In this article, a compressive sensing (CS) reconstruction algorithm is applied to data acquired from a nodding multi-beam Lidar system following a Lissajous-like trajectory. Multi-beam Lidar systems provide 3D depth information of the environment for applications in robotics, but the vertical resolution of these devices may be insufficient to identify objects, especially when the object is small and/or far from the robot. In order to overcome this issue, the Lidar can be nodded in order to obtain higher vertical resolution with the side-effect of increased scan time, especially when raster scan patterns are used. Such systems, especially when combined with nodding, also yield large volumes of data which may be difficult to store and mange on resource constrained systems. 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 sub-sample the imaged area and the data can be further reduced by simply not collecting each data point along the trajectory. The final depth image must then be reconstructed from the sub-sampled data. In this article, a CS reconstruction algorithm is applied to data collected during a fast and therefore low-resolution Lissajous-like scan. Experiments and simulations show the feasibility of this method and compare its results to images produced from simple nearest-neighbor interpolation.