Final answer:
The lambda phage switches from the lytic to the lysogenic state by using the proteins Cro and CI as repressors.
Step-by-step explanation:
The lambda phage switches from the lytic to the lysogenic state by using the proteins Cro and CI as repressors. During the lysogenic cycle, the phage genome integrates into the host genome, forming a prophage. The Cro protein helps maintain the lytic state by repressing the expression of genes required for lysogeny, while the CI protein helps maintain the lysogenic state by repressing the expression of genes required for the lytic cycle.