A mutation in the operator, where the repressor bonds, would prevent repression, no matter how functional the repressor was. Thus, gene expression for lactose metabolism would always be turned on, and the inducer would not be needed, since the repressor, which it causes to drop off DNA, would be unable to repress expression.
Work Step by Step
To understand this, consider that the normal role of the operator is to allow the repressor to bind in the absence of lactose and stop wasteful gene expression. Without binding, gene expression can proceed.