Cancer cell populations consist of phenotypically heterogeneous cells. Growing evidence suggests that pre-existing phenotypic differences among cancer cells correlate with differential susceptibility to anticancer drugs and eventually lead to a relapse. Such phenotypic differences can arise not only externally driven by the environmental heterogeneity around individual cells but also internally by the intrinsic fluctuation of cells. However, the quantitative characteristics of intrinsic phenotypic heterogeneity emerging even under constant environments and their relevance to drug susceptibility remain elusive. Here we employed a microfluidic device, mammalian mother machine, for studying the intrinsic heterogeneity of growth dynamics of mouse lymphocytic leukemia cells (L1210) across tens of generations. The generation time of this cancer cell line had a distribution with a long tail and a heritability across generations. We determined that a minority of cell lineages exist in a slow-cycling state for multiple generations. These slow-cycling cell lineages had a higher chance of survival than the fast-cycling lineages under continuous exposure to the anticancer drug Mitomycin C. This result suggests that heritable heterogeneity in cancer cells' growth in a population influences their susceptibility to anticancer drugs.