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Eigenchannel R-matrix calculations (including effects of long-range multipole interactions beyond the reaction volume) for Li- photodetachment partial cross sections from the vicinity of the Li 3s threshold to the Li 6s threshold (3.8 eV ≤ħω≤ 5.65 eV) are presented. Excellent agreement with the relative total cross section measurements of U. Berzinsh et al. [Phys. Rev. Lett. 74, 4795 (1995)] in the vicinity of the Li 3s and Li 3p thresholds is found. The calculated resonance structures are analyzed in detail. In particular, the energy region between the Li 4s and Li 5p thresholds (for which there are as yet no experimental measurements) is shown to have types of doubly excited resonances which are prominent only because of the nonhydrogenic Li+ core; such types are weak or absent in higher-energy regions as well as in H- photodetachment spectra.