Lateral Spectrum Splitting Concentrator Photovoltaics (LSSCPV) systems are being developed for high energy conversion efficiency. LSSCPV can concentrate available sunlight and laterally split a single beam into bands with different spectra, for absorption by solar cells with matched band gaps. Assemblies of an LSSCPV architecture including four p-n junctions were constructed, and tested by two institutes independently. One of the assemblies demonstrated verified module efficiency of 36.7%. In addition to the whole assembly efficiency, measurement methodology and testing procedure were proposed to assess the performance of each individual component in the system. The comparisons between the expected component efficiencies and the actually measured values, together with the comparisons between the independent assembly efficiency measurements by two organizations helped identify pathways to module efficiency greater than 40%.