We apply a general first-principles approach to derive the phase diagram of metallic lithium at ambient pressure between 0 and 350 K, including identification of candidate phases. We use ab initio random structure searching to identify competing phases and supplement the results with calculations of vibrational properties and relevant derived neutron diffraction patterns. Strong quantum nuclear effects are present, prompting a careful treatment of vibrations. We directly map the Born-Oppenheimer surface of Li, allowing the extension of the normal quasi-harmonic treatment of vibrations to a "quasi-anharmonic" approach, where the effects of anharmonicity are included. The Gibbs free energies of the fcc, bcc, hcp, and 9R phases are derived using a variety of equations of state. We find that the anharmonic contribution to the Gibbs free energies of Li phases is of the same order as the differences between phases. Anharmonicity also makes a noticeable difference to the 0-K phonon dispersion of the bcc phase, with the largest difference at the N-point phonon. The ordering of phase transitions that we find agrees with the calculations of Ackland et al. [Science 356, 1254 (2017)], even when anharmonic effects are included, suggesting that a quasi-harmonic treatment is sufficient for correct phase behavior. We show explicitly that the martensitic phase transition from close-packed to bcc lithium upon heating is driven by entropic contributions to the phonon free energy.
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