Absorption measurements allow the orientational order parameter of four dyes in the lyotropic chromonic liquid crystal di-sodium cromoglycate (DSCG) to be determined. The dye order parameters are small, except for dyes that intercalate between the DSCG molecules of the rod-like assemblies. The dye order parameters decrease with increasing temperature faster than the nematic order parameter of the DSCG assemblies. For intercalating dyes, the measured dye order parameter varies with the wavelength of the measurement because both intercalated and non-intercalated dye molecules contribute. On the contrary, measurements of the dye order parameter using fluorescence are sensitive only to intercalated dye molecules and produce values that reflect the order parameter of the DSCG assemblies. Therefore, the temperature and concentration dependence of the DSCG order parameter is also explored, since data of this kind on this often-studied system are lacking. Finally, the association constant of one of the intercalating dyes with the DSCG assemblies is determined, yielding a value considerably less than what is found for the same dye with DNA.