An experimental K-shell photodetachment study of Li(-) giving rise to doubly photoionized Li(+) ions has been carried out at the Advanced Light Source, using a collinear photon-ion beam apparatus. The experiment reveals dramatic structure, differing substantially both qualitatively and quantitatively from the corresponding processes above the 1s ionization threshold in Li and Li(+), as predicted by our enhanced R-matrix calculation. The experimental/theoretical comparison shows good agreement over some of the photon energy range, and also reveals some puzzling discrepancies.