The book of Lambda does not tell us that naturally occurring lysogens of are likely to be resistant as well as immune.

The most significant difference between bacteriophages functionally and ecologically is whether they are purely lytic (virulent) or temperate. Virulent phages can only be transmitted horizontally by infection, most commonly with the death of their hosts. Temperate phages can also be transmitted horizontally, but upon infection of susceptible bacteria, their genomes can be incorporated into that of their host's as a prophage and be transmitted vertically in the course of cell division by their lysogenic hosts. From what we know from studies with the temperate phage Lambda and other temperate phages, in laboratory culture, lysogenic bacteria are protected from killing by the phage coded for by their prophage by immunity; where upon infecting lysogens, the free temperate phage coded by their prophage is lost. Why are lysogens not only resistant but also immune to the phage coded by their prophage since immunity does not confer protection against virulent phages? To address this question, we used a mathematical model and performed experiments with temperate and virulent mutants of the phage Lambda in laboratory culture. Our models predict and experiments confirm that selection would favor the evolution of resistant and immune lysogens, particularly if the environment includes virulent phage that shares the same receptors as the temperate. To explore the validity and generality of this prediction, we examined 10 lysogenic from natural populations. All 10 were capable of forming immune lysogens, but their original hosts were resistant to the phage coded by their prophage.