The lac operon is an brilliant example of negative control or negative regulation of gene expression in which they bound repressor stops transcription of the structural genes. The Positive control or positive regulation of gene expression is when the regulatory protein binds to enhances and DNA the rate of transcription.  In that case the regulatory protein is called as an activator.  The CAP or CRP included in regulating the lac operon is a good instance of an activator. Thus the lac operon is subject to both positive and negative control.