The effects of fast electron confinement and plasma temperature on the lower hybrid current ramp-up efficiency are investigated. The production of reverse runaways in a toroidal geometry is calculated with a Monte Carlo particle following code, which includes collisions and both neoclassical and relativistic effects. When anomalous fast electron diffusion in the configuration space is taken into account, the ramp-up efficiency is found to be enhanced for increasing loss rate of runaway electrons. The enhancement is in accordance with a simple analytical model that expresses the efficiency as a function of the average runaway electron confinement time and the runaway fraction of current carrying electrons. A larger runaway production rate is found for the electrons orbiting on outer magnetic surfaces, because their trapping region in velocity space is wider. The runaway rate is also significantly enhanced, as the thermal velocity is increased up to and above one sixth of the runaway velocity v_R. The range of the phase velocity spectrum where the waves efficiently ramp up the current in large tokamaks is limited by these effects to velocities below 1.3v_R