Below is a pictorial representation about how lactose transport and lactose metabolism is done in the cell. The structural genes are arranged adjacent to each other and are expressed together in a polycistronic message in the lac operon. Lac operon genes including lac Z gene are regulated by negative and positive regulatory mechanisms. Another mechanism by which production of beta-galactosidase is regulated is by induction. Induction of lac operon occurs in the presence of lactose and in the absence of glucose in the medium.
Induction also occurs because of the presence of allolactose.
Basal levels of beta-galactosidase is always present, so when glucose is not around, lactose metabolism can occur. Beta-galactosidase allows the conversion of lactose to allolactose in transglycosylation reaction. Below is a picture of lac operon and its various components. The picture below gives you a representation on how repression of lac operon works. Below is a representation on how induction in lac operon works.