Lac repressor is a DNA-binding protein. It inhibits the expression of genes that codes for the expression of proteins involved in the metabolism of lactose in bacteria.
The Lac repressor binds to the operator and partially overlaps with the promoter inhibiting the transcription of the lac operon.
Lac operon is a group of genes encoding proteins that allow the bacteria to use lactose as an energy source.
It is coded by the āiā gene in the lac operon. It inhibits the transcription of RNA polymerase by binding to the operator region present adjacent to the promoter region.
At the bound stage, lac repressor gets in RNA polymerase's way keeping it from the transcription of the operon.
In presence of lactose, the lac repressor binds tightly to the operator, preventing transcription by the polymerase.
The lac operon senses lactose through the presence of allolactose, an isomer of lactose.