Final answer:
The regulatory protein that binds to the promoter of the lac operon and allows transcription to proceed is called the catabolite activator protein (CAP) or CAMP receptor protein (CRP).
Step-by-step explanation:
The regulatory protein that binds to the promoter of the lac operon and allows transcription to proceed is called the catabolite activator protein (CAP) or CAMP receptor protein (CRP). When glucose levels are low and lactose is present, the accumulating cyclic AMP (cAMP) binds to CAP and the complex then binds to the promoter region, increasing the binding ability of RNA polymerase and promoting transcription of the lac operon.