Self-consistent-field and configuration interaction procedures are used to calculate the potential energy curves and the non-adiabatic radial and rotational couplings for the Li₂²⁺ system. The lowest six ¹ Sigma _g, four ¹ Pi _g and one 1 Delta _g states are included. The standard perturbed stationary-state approach is employed to study collisions between Li⁺ ions for the interaction energies between 10 and 80 keV. The calculated charge transfer cross sections are in good agreement with the observations of Li²⁺ formation for energies above 35 keV.