Lactose plays dual role in lac operon. Firstly, it acts as an inducer for lac operon since it regulates the switching on and off of the operon. Secondly it acts as substrate for the enzyme beta galactosidase.
Lac operon is said to be under negative regulation because the regulation of operon is controlled by repressor protein synthesised by i gene. In otherwords, when the operon is regulated by repressor, it is known as negative regulation.