Isogenic bacteria can exhibit a range of phenotypes, even in homogeneous environmental conditions. Such nongenetic individuality has been observed in a wide range of biological processes, including differentiation and stress response. A striking example is the heterogeneous response of bacteria to antibiotics, whereby a small fraction of drug-sensitive bacteria can persist under extensive antibiotic treatments. We have previously shown that persistent bacteria enter a phenotypic state, identified by slow growth or dormancy, which protects them from the lethal action of antibiotics. Here, we studied the effect of persistence on the interaction between Escherichia coli and phage lambda. We used long-term time-lapse microscopy to follow the expression of green fluorescent protein (GFP) under the phage lytic promoter, as well as cellular fate, in single infected bacteria. Intriguingly, we found that, whereas persistent bacteria are protected from prophage induction, they are not protected from lytic infection. Quantitative analysis of gene expression reveals that the expression of lytic genes is suppressed in persistent bacteria. However, when persistent bacteria switch to normal growth, the infecting phage resumes the process of gene expression, ultimately causing cell lysis. Using mathematical models for these two host-phage interactions, we found that the bacteria's nongenetic individuality can significantly affect the population dynamics, and might be relevant for understanding the coevolution of bacterial hosts and phages.