Excitation energies of the [Xe]nd (n = 5-9), [Xe]ns (n = 6-10), [Xe]np (n = 6-9), [Xe]nf (n = 4-8), and [Xe]ng (n = 5-8) states in La III, where [Xe] = 1s(2)2s(2)2p(6)3s(2)3p(6)3d(10)4s(2)4p(6)4d(10)5s(2)5p(6), are evaluated. Electric dipole matrix elements for the allowed transitions between the low-lying [Xe]nd, [Xe]ns, [Xe]np, [Xe]nf, and [Xe]ng states in the La III ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar and tensor polarizabilities of the states listed above are evaluated. The uncertainties of the recommended values are estimated. Electric quadrupole and magnetic dipole matrix elements are calculated to determine lifetimes of the 5d(5/2) and 6s metastable levels. The ground-state E1, E2, and E3 static polarizabilities are calculated. This work provides recommended values critically evaluated for their accuracy for a number of La III atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.