The lac operon actually uses both Negative and positive systems.
There are 2 types of regulation of the lac operon.
Negative Regulation- When the expression of genetic information is quantitatively decreased by the presence of specific regulatory element, it is called as negative regulation.
Positive Regulation- When the expression of genetic information is quantitatively increased by the presence of specific regulatory element, it is called as positive regulation
The lac operon is a negative control system because expression is typically blocked by an active repressor (the lac repressor) that turns off transcription. The lac repressor binds to the operator region and negatively controls (prevents) transcription.
However, when CAP (catabolite gene activating protein) binds upstream of this operator region near the promoter and transcription increases, this is an example of a positive control system. We see this positive control of transcription happen when glucose levels decline.
