First principles calculations of mutual neutralization in and collisions have been performed for low energies (0.68-50.0 eV). A diabatic representation is used for eight electronic states determined directly within an ab initio calculation. For the comparison with the recent merged-beam experiment the finite acceptance angle of the detector has been taken into account. An improved ionic diabatic curve, corrected for deficiencies in the ab initio electron affinity of H, has also been used. The large cross section at low energy for this mutual neutralization is due predominantly to the almost optimal efficiency for the non-adiabatic transition to the neutral Li(3s)H(1s) state. The calculated cross section exceeds experiment by no more than about 20%, indicating that the neutral-ionic diabatic crossings and couplings are accurately evaluated by the ab initio approach.