The correct option is
E Regulator protein to switch off structural gene transcription
According to lac operon concept, regulator gene regulates the expression of structural genes by its protein product that is mostly transcription factor. These transcription factors, the regulatory protein, bind to the operator region which is located just upstream the binding site of the RNA polymerase and hence, prevent the binding and transcription. The operator is a DNA sequence present between the promoter region and the first coding gene. This operator region serves as repressor protein binding site, not for repressor or regulatory gene itself. This makes statement C and D incorrect.
The gene that codes for any RNA / protein product which does not serve as regulatory protein is known as a structural gene. The lac z, lac y and lac a genes in lac operon are the structural genes. A corepressor inhibits the expression of genes not by directly binding to DNA but instead indirectly regulates gene expression by binding to repressors; they are present in the repressible operon. This makes statement A incorrect.
A molecule, that regulates gene expression by binding to repressors or activators to prevent or start the transcription respectively, is inducer. Allolactose serves as an inducer in the lac operon and binds to the repressor, not to operator gene, and decreases the repressor's affinity for the operator site; thereby facilitating transcription. This makes statement B incorrect. Option E is the correct answer.