Gene regulation governing lactose operon of E. coli that involves the lac i gene products is

Gene regulation governing lactose operon of E. coli that involves the Lac i gene products is negative and inducible because its repressor protein prevents transcription.
Lac i gene produces an inhibitor or repressor that induces negative regulation of lac operon. 
The repressor binds to the operator gene and stops its working. Repressor is meant to block the operator gene, so that structural genes are unable to form mRNA, thus stopping the transcription of genes. 
On the other hand, lactose operon is inducible. It is a regulated unit of genetic material which is switched on in response to the presence of a chemical.