In this paper, a novel method for the lossless compression of the interferometer hyperspectral instrument Large Aperture Static Imaging Spectrometer (LASIS) data is presented. This scheme rests upon the combination of data rearrangement and band ordering of LASIS three dimensional image and the recently presented CCSDS-123 lossless multispectral & Hyperspectral image compression standard. Firstly, the LASIS data is rearranged from the photo acquisition coordinate to the optical path difference (OPD) image coordinate by the rearrange approach to remove the interference information superimposed on the image. Then the OPD band is reordered according to the interferogram characteristic to improve the correlation between adjacent bands. Finally, the reordered OPD band data is processed using the CCSDS-123 standard. Several experiments were conducted to investigate the performance of the proposed compression scheme in the end. Experimental results suggest that this proposed compression scheme gives 31% higher compression ratio than using the standard alone.