The inducer in the lac operon is allolactose. If lactose is present in the medium, then a small amount of it will be converted to allolactose by a few molecules of β-galactosidase that are present in the cell. Allolactose binds to the repressor and decreases the repressor's affinity for the operator site.
However, when lactose and glucose are both available in the system, the lac operon is repressed. This is because glucose actively prevents the induction of lacZYA.