We present cross sections for the radiative charge transfer process Li(2s) + H+→Li+(1s2)+ H(1s) + hω for collision energies between 0.1 meV and 1O eV and rate coefficients for temperatures between 1O and 40,000 K. At 300 K, the rate coefficient is 1.3 x 10-13 cm-3 s-1. The results are obtained through a fully quantum-mechanical method using completely ab initio molecular data. Cross sections for the total collision-induced radiative decay, radiative charge transfer plus radiative association, from the entrance Li(2s) + H+ channel are calculated with the optical potential method. Radiative charge transfer dominates radiative association for the considered collision energies, but direct charge transfer will become important at higher energies. The emission spectrum, which has a peak at wavelengths near t58 nm, due to radiative charge transfer is given for several collision energies. Implications to the lithium ionization fraction in the postrecombination era of the early universe are discussed.