The host cell may lyse or may continue to divide and replicate both itself and the prophage.
Lytic cycle:
The infecting phage kills the host cell at the end of the lytic cycle, also known as a virulent infection, to create a large number of its own offspring. The phage genome immediately produces early proteins that degrade the host DNA after being injected into the host cell, enabling the phage to take over the cellular machinery.
The remaining proteins needed to construct fresh phage particles are subsequently synthesized by the phage using the host cell. The new genetic material is packed into the head while new daughter phage particles are built, and the heads and sheaths are created independently. In the course of this process, phage enzymes gradually weaken the host cells, which eventually burst, dispersing 100–200 additional phage progeny into the environment.
Lysogenic cycle:
The lysogenic cycle, also known as temperate or non-virulent infection, uses the host cell as a haven where it can survive in a latent state. It does not harm the host cell. After the phage DNA is injected into the host cell, it uses integrases encoded by the phage to integrate into the host genome, at which point it becomes known as a prophage.
The host cell divides for the duration that it is there and does not create the proteins necessary to make progeny, at which point the prophage genome is passively copied alongside the host genome. The bacterial hosts are typically somewhat unaffected by this procedure because the phage genome is typically quite tiny.
I understand the question you are looking for is this:
As a consequence of infection by a temperate bacteriophage such as lambda, the host cell
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