The electron capture processes in Li2 + + H collisions have been investigated by using the quantum-mechanical molecular-orbital close-coupling method and the two-center atomic-orbital close-coupling method in the energy ranges of 10-8–10 keV/u and 0.1–300 keV/u, respectively. The capture to singlet and triplet systems of states of Li+(1s,n l 2S + 1L) is considered separately. Total, n,S-resolved and n,l,S-resolved electron capture cross sections are calculated and compared with the results of available experimental and theoretical studies. The present calculations show that the n = 2 shell of Li+ is the main capture channel for all energies considered in both the singlet and triplet case. While for collision energies E> 5 keV/u, the cross sections for capture to the n = 2 manifold are of the same order of magnitude for both the singlet and triplet states (with the 2p capture cross section being dominant), for energies below ~5 keV/u the cross sections for capture to the n = 2 triplet manifold is significantly (more than three orders of magnitude at 0.1 keV/u) larger than that for capture to the n = 2 singlet manifold of states (with the 2s capture cross section being dominant). The capture dynamics at low collision energies is discussed in considerable detail, revealing the important role of rotational couplings in population of l> 0 capture states. The elastic scattering processes have been studied as well in the energy range of 10-8–1 keV/u. The calculated elastic scattering cross section is much larger than the electron capture cross section in both the singlet and triplet case. However, as the collision energy increases, the difference between the elastic and electron capture cross sections decreases rapidly.