The response of liquid xenon to low-energy electronic recoils is relevant in the search for dark-matter candidates which interact predominantly with atomic electrons in the medium, such as axions or axionlike particles, as opposed to weakly interacting massive particles which are predicted to scatter with atomic nuclei. Recently, liquid-xenon scintillation light has been observed from electronic recoils down to 2.1 keV, but without applied electric fields that are used in most xenon dark-matter searches. Applied electric fields can reduce the scintillation yield by hindering the electron-ion recombination process that produces most of the scintillation photons. We present new results of liquid xenon's scintillation emission in response to electronic recoils as low as 1.5 keV, with and without an applied electric field. At zero field, a reduced scintillation output per unit deposited energy is observed below 10 keV, dropping to nearly 40% of its value at higher energies. With an applied electric field of $450\text{ }\text{ }\mathrm{V}/\mathrm{cm}$, we observe a reduction of the scintillation output to about 75% relative to the value at zero field. We see no significant energy dependence of this value between 1.5 and 7.8 keV. With these results, we estimate the electronic-recoil energy thresholds of ZEPLIN-III, XENON10, XENON100, and XMASS to be 2.8, 2.5, 2.3, and 1.1 keV, respectively, validating their excellent sensitivity to low-energy electronic recoils.