MEMS light detection and ranging (LiDAR) is becoming an indispensable sensor in vehicle environment sensing systems due to its low cost and high performance. The beam scanning trajectory, sampling scheme and gridding are the key technologies of MEMS LiDAR imaging. In Lissajous scanning mode, this paper improves the sampling scheme, through which a denser Cartesian grid of point cloud data at the same scanning frequency can be obtained. By summarizing the rules of the Cartesian grid, a general sampling scheme independent of the beam scanning trajectory patterns is proposed. Simulation and experiment results show that compared with the existing sampling scheme, the resolution and the number of points per frame are both increased by 2 times with the same hardware configuration and scanning frequencies for a MEMS scanning mirror (MEMS-SM). This is beneficial for improving the point cloud imaging performance of MEMS LiDAR.