Experiments with simultaneous lower hybrid current drive and ion cyclotron resonance frequency heating of minority protons in JET deuterium plasmas showed efficient coupling of LH power to the MeV energy anisotropic protons. Such interaction represents parasitic loss of LH power, intended for electron current drive, to the proton population, with important implications for the efficiency of LH current drive schemes in fusion devices containing high energy charged fusion products. We solve the hot-plasma dispersion relation in the LH range of frequencies for plasmas containing high energy minority anisotropic protons and electrons, and find that multiple solutions of the dispersion relation with perpendicular refractive index n⊥>40 exist in the plasma centre due to the presence of the protons. These hot-plasma modes give ≈20%-40% damping of LH input power onto the protons by perpendicular Landau damping. Combinations of background plasma and LH antenna parameters exist for which no solutions of the LH dispersion relation are found with n⊥20, thus reducing damping of LH power to the protons to ≈5%-10%. This suggests ways of reducing the parasitic loss of LH power to high energy charged fusion products.