We determine the radial dipole moment between the 2S and 2P states of atomic lithium by analyzing the long-range vibrational eigenenergies of the singly excited diatomic molecule. The result can be expressed in terms of the 2P12 radiative lifetime of Li7, which is found to be 27.102(2)(7) ns. This result agrees with most current atomic-structure calculations and resolves the long-standing disagreement with previous experiment. The current level of precision is sensitive to relativistic effects in the atomic-structure calculation and to non-Born-Oppenheimer and radiation retardation effects in the molecule.