The large-aperture static imaging spectrometer (LASIS) is an interference spectrometer with high device stability, high throughput, a wide spectral range, and a high spectral resolution. One frame image of the original data cube acquired by the LASIS shows the image superimposed with interference fringes, which is distinctly different from traditional hyperspectral images. For compression studies using this new type of data, a lossless compression scheme that combines a novel data rearrange method and the lossless multispectral and hyperspectral image compression standard CCSDS-123 is presented. In the rearrange approach, the LASIS data cube is rearranged such that the interference information overlapped on the image can be separated, and the results are then processed using the CCSDS-123 standard. Then, several experiments are conducted to investigate the performance of the rearrange method and examine the impact of different CCSDS-123 parameter settings for the LASIS. The experimental results indicate that the proposed scheme provides a 32.9% higher ratio than traditional rearrange methods. Moreover, an adequate parameter combination for this compression scheme for LASIS is presented, and it yields a 19.6% improvement over the default settings suggested by the standard.