The genes and important sequences for the regulation of the lac operon are organized such that several mediators can fine tune expression of the three genes in the operon itself—lacZ, lacY, and ...
The operon is regulated by Lac repressor, the product of the lacI gene, which is transcribed from its own promoter (PI). The repressor inhibits transcription by binding to the lac operator (O).
Can the presence of glucose itself activate the genes that will break it down? It does in bacteria through a process known as positive transcription control.