Quantifying socioeconomic inequalities in health in absolute terms is of prime interest for decision-making and for international comparisons. The Slope Index of Inequality (SII), an index that quantifies absolute socioeconomic inequalities, was recently formalized, particularly in the context of mortality differences measured in the rate or hazard scale. However, absolute inequalities using either rates or hazards do not translate into a time dimension, which makes their interpretation difficult for policy makers. We propose an extension of the SII in terms of the expected number of life years lost before an upper age, as well as its decomposition by cause of death. The SII in the life years lost metric quantifies the extent to which life expectancy is shortened when comparing the higher and lower ends of the socioeconomic scale. The methodology proposed builds on recent developments in survival analysis for decomposing the number of life years lost according to cause of death using a pseudo-value approach. We illustrate our proposal using a representative 1% sample of the French population. The SII in the life years lost metric is easily understood, and the decomposition of the all-cause mortality SII into parts attributable to given causes provides a sound estimation of the burden of different causes of death on absolute socioeconomic inequalities in mortality.