The presence of a mutant lac repressor that could not bind lactose would result in no transcription even when lactose was present because the mutant repressor would remain bound to the lac operator
The transcription of lac operator is controlled by the lac repressor. When lactose is present, the lac repressor normally will bind to the lactose, removing itself from the lac operator so it could be transcripted.
In this case, the mutation makes the lac repressor keep binding to the lac operator so the result would be no transcription even when lactose present.
The answer to the question you asked is ..... Microfilaments.
