Lithium cation and anion diffusion constants (D-Li and D-Anion) are plotted versus ionic conductivity (sigma) (sigma-D relation) for lithium organic electrolyte solutions which are important to investigate Li secondary batteries. Lithium salts studied are LiPF6, LiBF4, LiN(SO2CF3)(2) (LiTFSA), LiN(SO2C2F5)(2) (LiBETI), LiC4BO8 (LiBOB), LiSO3CF3 and Li(2)B(12)F(1)2. Main organic solvents are propylene carbonate (PC), ethylene carbonate (EC), gamma-butyrolactone (GBL), diethyl carbonate (DEC), four glymes and polyethylene glycol (PEG) dimethyl ethers of average molecular weights of 400 and 1,000. Mixing effects of two solvents are shown for EC-DEC-LiPF6 systems. In total, about 20 organic electrolyte solutions were studied. In addition, for six binary ionic liquid systems, sigma-D relations are plotted. Values for the degree of apparent ion dissociation (alpha) were calculated from the D-Li, D(Anio)n and s using the Nernst-Einstein (NE) relation and are plotted against sigma (sigma-alpha relation). The number of charge-carrying ions (Ncarrier) was estimated from the alpha and salt concentration, and plotted versus sigma (sigma-Ncarrier relation). To estimate the velocity of ions, the sigma-D solvent relations are plotted. Also, the apparent lithium transference number (t(Li)) obtained simply from the D-Li and D-anion values are plotted versus sigma (sigma-tLi relation). While we have already reported all the data in our previous papers, we did not plot directly the ion diffusion constants and other parameters versus ionic conductivity. In this paper, the importance of the direct relations of sigma-D, sigma-alpha, and sigma-Ncarrier is demonstrated to understand functions of lithium electrolyte solutions. The numerical data are freely available in Supplementary Information (SI), covering broad aspects of the fundamental and practical lithium electrolyte solution systems. We believe that they will contribute to the research and development for next generation Li battery systems. (C) 2017 Elsevier Ltd. All rights reserved.