On the basis of the quasi-linear theory of tokamak current drive by lower hybrid waves, a velocity diffusion process is introduced for electrons that are not Landau resonating with the waves. This effect is connected to the time dependence of the wave field auto-correlations which can be determined by non-linear terms (only postulated here) or by the geometric effect of a sharp wave beam of finite toroidal width. In both cases, the role of non-resonant electron velocity diffusion is important in evaluating the driven current and the absorbed power correctly (as it may fill the gap in velocity space between bulk and resonant tail electrons). It also implies the presence of a fast REF-runaway electron tail above the Landau resonance. This tail requires a treatment which includes relativistic effects, as well as, 2-D velocity space and cross field transport of fast electrons, but preliminary considerations indicate that it does not depend much on the wave spectrum (or on the accessibility limit). Finally, the temperature scaling of the current drive efficiency is found to be different from the classical result obtained in the usual quasi-linear theory.