Replicative lifespan, the number of replications a cell undergoes before entering senescence, is one of the main modulators of aging. One of the hallmarks of replicative lifespan in mammalian cells is its heterogeneity even within an isogenic population. One of the mechanisms that contribute to senescence is telomere shortening. In most of the somatic cells, telomere lengths correlate with cellular life span. Yet, our understanding of the relation between telomere dynamics and senescence is still lacking as previous models could not explain the experimentally observed replicative lifespan distributions and sister cell correlations solely by continuous telomere shortening. In this work, we develop a mathematical model of telomere replication and shortening. We account for the asymmetry of the telomere replication mechanism and explore its impact on growth capacity and lineage correlations.