Disclosed is a liquid electrolyte for use in lithium-ion, lithium-metal, and lithium-sulfur batteries, in which the liquid electrolyte comprises at least one organic nonlinear carbonate, at least one lithium salt, and at least one cyclic sulfoxide, and in which the liquid electrolyte does not comprise a combination of propylene carbonate, tetrahydrothiophene-1-oxide, and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). Also disclosed is a lithium secondary battery comprising an anode, a cathode, a separator, and the liquid electrolyte for use in lithium-ion, lithium-metal, and lithium-sulfur batteries.