The statistical acceleration of electrons along an ambient magnetic field by large-amplitude lower-hybrid turbulence is discussed. Perturbations driven by a crossfield current and propagating nearly perpendicular to the applied magnetic field are considered. It is assumed that the instability saturates rapidly and that the fluctuating electric field is predominantly electrostatic. This work is not concerned with the detailed saturation mechanism, but rather with what happens to the electrons after the turbulence has saturated. If the turbulence is characterized by a spectrum of small parallel wavenumbers, such that the parallel phase velocity of the waves is greater than the electron thermal velocity, then the turbulence can only accelerate electrons moving with large velocities along the magnetic field. The qusai-linear diffusion equation is solved using a Green's function technique, assuming a power law spectral energy density. The time evolution of an initial Maxwellian distribution is given and the time rate of change of the mean electron energy is calculated for various cases.