Lithium alloying reactions are beneficial in promoting uniform plating and stripping of lithium metal in all-solid-state batteries. First-principles calculations are performed to predict thermodynamic, kinetic, and mechanical properties of lithium and several important Li-M alloys (M = Mg, Ag, Zn, Al, Ga, In, Sn, Sb, and Bi). While the Li-Mg binary system forms a solid solution, most other lithium-metal alloys prefer stoichiometric intermetallic compounds with common local motifs that enable fast Li diffusion. Lithium and Li-rich alloys exhibit an unusually flat energy landscape along paths that connect BCC to close-packed structures like FCC and HCP, with important implications for mechanical properties. Very low migration barriers for Li diffusion that rival those of superion conductors are predicted, both in pure Li and in Li-M intermetallics. However, vacancy concentration, which is crucial for substitutional diffusion, is predicted to be low in metallic Li and most Li-M intermetallics. Compounds such as B32 LiAl and LiGa as well as D03 Li3Sb and Li3Bi exhibit structural vacancies at higher ends of their voltage windows, which together with low migration barriers leads to exceptionally high Li mobilities. In the Li-Mg solid solution, the addition of Mg is found to decrease the vacancy tracer diffusion coefficient by an order of magnitude.