Experiments with antihydrogen ((H) over bar) for a study of matter-antimatter symmetry and antimatter gravity require ultracold (H) over bar to reach ultimate precision. A promising path towards antiatoms much colder than a few kelvin involves the precooling of antiprotons by laser-cooled anions. Because of the weak binding of the valence electron in anions-dominated by polarization and correlation effects-only few candidate systems with suitable transitions exist. We report on a combination of experimental and theoretical studies to fully determine the relevant binding energies, transition rates, and branching ratios of the most promising candidate La-. Using combined transverse and collinear laser spectroscopy, we determined the resonant frequency of the laser cooling transition to be nu = 96.592 713(91) THz and its transition rate to be A = 4.90(50) x 10(4) s(-1). Using a novel high-precision theoretical treatment of La- we calculated yet unmeasured energy levels, transition rates, branching ratios, and lifetimes to complement experimental information on the laser cooling cycle of La-. The new data establish the suitability of La- for laser cooling and show that the cooling transition is significantly stronger than suggested by a previous theoretical study.