We present the rest-frame optical luminosity function (LF) of red-sequence galaxies in 16 clusters at 0.4 < z < 0.8 drawn from the ESO Distant Cluster Survey (EDisCS). We compare our clusters to an analogous sample from the Sloan Digital Sky Survey (SDSS) and match the EDisCS clusters to their most likely descendants. We measure all LFs down to M similar to M* + (2.5 -3.5). At z < 0.8, the bright end of the LF is consistent with passive evolution but there is a significant buildup of the faint end of the red sequence toward lower redshift. There is a weak dependence of the LF on cluster velocity dispersion for EDisCS but no such dependence for the SDSS clusters. We find tentative evidence that red-sequence galaxies brighter than a threshold magnitude are already in place, and that this threshold evolves to fainter magnitudes toward lower redshifts. We compare the EDisCS LFs with the LF of coeval red-sequence galaxies in the field and find that the bright end of the LFs agree. However, relative to the number of bright red galaxies, the field has more faint red galaxies than clusters at 0.6 < z < 0.8 but fewer at 0.4 < z < 0.6, implying differential evolution. We compare the total light in the EDisCS cluster red sequences to the total red-sequence light in our SDSS cluster sample. Clusters at 0.4 < z < 0.8 must increase their luminosity on the red sequence (and therefore stellar mass in red galaxies) by a factor of 1 -3 by z = 0. The necessary processes that add mass to the red sequence in clusters predict local clusters that are overluminous as compared to those observed in the SDSS. The predicted cluster luminosities can be reconciled with observed local cluster luminosities by combining multiple previously known effects.