We investigate parallel electron acceleration due to inertial Alfvén wave pulses in the presence of Lorentzian (kappa) distribution functions which possess high-energy tails. A linear kinetic dispersion relation for inertial Alfvén waves is derived whose solutions are used to guide the analysis of the simulation results. The dispersion relation solutions show that the parallel phase velocity of linear waves is unchanged when Lorentzian distribution functions are considered instead of Maxwellian distribution functions. The solutions also indicate that Landau damping is increased for low values of spectral index, κ, implying that wave-particle interactions are enhanced for Lorentzian distribution functions. We test this hypothesis by performing self-consistent kinetic simulations and show that the energy content of resonant beam electrons significantly increases with decreasing κ. The dependence of this process on pulse amplitude and perpendicular scale length is investigated, and it is shown that for the same pulse parameters, resonant electron beams are generated more efficiently in a Lorentzian plasma compared to a Maxwellian plasma. The energy range of resonant beam electrons are also presented, and it is noted that for low values of κ it is possible to generate electrons with energy of a few keV, even for relatively small-amplitude pulses with peak perpendicular electric fields of the order of 20 mV/m. We also show that the percentage of wave Poynting flux which is converted into electron energy flux depends upon the value of κ, the perpendicular scale length, and the initial amplitude of the inertial Alfvén wave.