We use the lag-luminosity relation to calculate self-consistently the redshifts, apparent peak bolometric luminosities L_B, and isotropic energies E_iso for a large sample of BATSE gamma-ray bursts. We consider two different forms of the lag-luminosity relation; for both forms the median redshift for our burst database is 1.6. We model the resulting E_iso sample with power law and Gaussian probability distributions without redshift evolution, both of which are reasonable models. The power law model has an index of alpha_E=1.76+/-0.05 (95% confidence), where p(E_iso) propto E_iso^(-alpha_E). The simple universal jet profile model suggested but did not require alpha_E=2, and subsequent physically reasonable refinements to this model permit greater diversity in alpha_E, as well as deviations from a power law; therefore our observed E_iso probability distribution does not disprove the universal jet model.

25 pages, 9 figures, to be published in ApJ, data available at http://cossc.gsfc.nasa.gov/analysis/lags/