The average white male born in 1900 earned 2.6 times more labor income over their lifetime than the average Black male. This gap is nearly twice as large as the more commonly studied cross-sectional Black-white earnings gap because 48% of Black males born in 1900 died before the age of 30 as compared to just 26% of white males. We calibrate a model of optimal consumption in a world with mortality risk to data describing the life-cycle earnings and survival probabilities of Black and white males born between 1900 and 1970. We find that convergence in Black and white mortality rates led to a 50% reduction in Black-white welfare gaps between the 1900 and 1920 birth cohorts, even as cross-sectional Black-white income gaps for those cohorts remained relatively constant. However, the Black-white welfare gap stagnated for the 1920 to 1970 birth cohorts as gaps in Black-white life expectancy and income remained stable and large.