Based on cosmological simulations, we model Lyman continuum emission from a sample of 11 high-redshift star-forming galaxies spanning a mass range of a factor 20. Each of the 11 galaxies has been simulated both with a Salpeter and a Kroupa initial mass function (IMF). We find that the Lyman continuum luminosity of an average star-forming galaxy in our sample declines from z = 3.6 to 2.4 due to the steady gas infall and higher gas clumping at lower redshifts, increasingly hampering the escape of ionizing radiation. The galaxy-to-galaxy variation of apparent Lyman continuum emission at a fixed redshift is caused in approximately equal parts by the intrinsic variations in the Lyman continuum emission and by orientation effects. The combined scatter of an order of magnitude can explain the variance in the far-UV spectra of high-redshift galaxies detected by Shapley and coworkers. Our results imply that the cosmic galactic ionizing UV luminosity is monotonically decreasing from z = 3.6 to 2.4, curiously anticorrelated with the star formation rate in the smaller galaxies, which on average rises during this redshift interval.