Final answer:
The untrue statement about the lac operon is that it produces a diffusible product that can regulate the expression of the operon. Instead, the lacI gene produces a repressor that binds to the operator to control transcription based on lactose presence.
Step-by-step explanation:
The statement about the lac operon that is not true is: it produces a diffusible product that can regulate the expression of the operon. The lacI gene produces the lac repressor, which operates to bind the operator region and prevents transcription when lactose is not present. A mutation in one of the structural genes of the lac operon, such as lacZ, lacY, or lacA, would typically result in a loss of function for the mutated gene's protein product, affecting the ability of the bacterium to metabolize lactose. If the mutation occurs in lacZ, for example, the bacterium would lose the ability to produce beta-galactosidase, which is necessary to break down lactose into glucose and galactose.