The authors present theoretical results for Li³⁺-H(2s) and Li³⁺-H(1s) total charge exchange cross sections at low energies (130 eV-18 keV and 500 eV-10 keV, respectively). Exact OEDM molecular energies and the Landau-Zener method are employed in the study of the first reaction. The error introduced in the cross section by the molecular curves in the context of the Landau-Zener approximation is estimated by error propagation analysis. The total cross section for the latter reaction obtained in previous works is extended to low energies. The results, which show quite a large increase with the collision energy, are compared with other theoretical data.