Under which conditions are the lac structural genes expressed most efficiently?

Lac genes are most effectively expressed in presence of Lactose and its analogs when glucose is absent.

Explanation:

A unit of prokaryotic gene expression and regulation, which includes structural genes and regulatory sequences recognized by regulatory gene product is called operon.

Lac structural genes are a part of Lac operon. The Lac operon consists of three, structural genes, an operator and a promoter. The product of Lac operon is involved in the conversion of disaccharide lactose into glucose and Galactose.

Lactose and its analogs are inducers of Lac operon. So, the structural genes are best expressed in presence of Lactose. Glucose and galactose are repressors of lac gene so the genes are repressed in presence of glucose.