Many experiments have proved the effectiveness of lower hybrid waves for current drive (CD) and current density profile control in tokamaks. However, fusion generated a-particles may be accelerated well beyond their birth velocity and may damp the wave energy, thus reducing the CD efficiency. This effect is absent at high frequency (8 GHz), but such a high frequency is undesirable for technical reasons. Therefore in this paper we calculate, at different frequencies (<8 GHz), the competition in the absorption between alphas and electrons in ITER-FEAT scenarios using a quasi-linear (QL) model for the a distribution function and full ray tracing in toroidal plasmas for the lower hybrid propagation. The use of the QL model for alpha-particles is mandatory to evaluate the tail in the distribution function, which, if very energetic, could affect the ITER first wall. The results of the present calculation show that, to limit the alpha absorption to few percents, a bottom frequency of 5 GHz is required. The CD efficiency provided for these scenarios by our numerical model is also presented.