Absolute total and differential cross sections have been measured for neutral Li formation in single collisions of ${\mathrm{Li}}^{+}$ on ${\mathrm{H}}_{2}$ from 1 to 5 keV. Total cross sections were obtained by direct integration of measured differential cross sections and are in good agreement with earlier cross-sectional measurements. A comparison of the differential cross sections plotted as a function of the reduced variables $\ensuremath{\theta}\mathrm{sin}\ensuremath{\theta}d\ensuremath{\sigma}/d\ensuremath{\Omega}$ vs $E\ensuremath{\theta}$ is also presented with a comparison of the maximum of the curves of the present data. Theoretically, we report state to state and summed charge transfer at collision energies ranging from 0.1 to 25 keV/amu. Cross sections were calculated using a nonadiabatic time-dependent direct approach for study of ion-atom and ion-molecule interaction processes. We verify that the main electron-capture channel is in the $n=2$ state of Li with a large probability for electron capture for impact parameters below 2 a.u. for collisions on both H and ${\mathrm{H}}_{2}$ in the so-called rotational region of the collision. In the case of atomic hydrogen, the electron-capture probability into the $2s$ and $2p$ states shows an oscillating behavior that smooths out when summed. For the molecular case, we find that for projectile energies larger than 1 keV, ionization effects become important. Our results show good agreement when compared to other available experimental and theoretical data.