In this report, we propose the "lossless coding gain" as a new objective criterion to theoretically evaluate performance of the lossless wavelet transforms(LWT). Relationship between the "lossless coding gain" and existing "coding gain(lossy coding gain)" is also explicitly described. It becomes possible to theoretically evaluate lossless-lossy unified coding methods based on the LWT under the unified criterion- "lossless coding gain" and "lossy coding gain". Experiments in the report include applications of the two-dimensional(2D)LWT to some standard images and 2D AR(1)model. Effectiveness of the "optimum bit allocation" in the quantization procedure is also described.