How does lactose affect the rate of transcription?

Answer 1

Are you talking about the lac operon?

When lactose is present, allolactose binds to the repressor protein (which was originally bound to the operator section of the DNA), and the protein lets go of the DNA. This allows transcription to continue (as the protein was blocking it when it was bound to the DNA).

So, transcription of the lactose-digesting enzymes occurs, and the enzymes digest lactose. When the lactose is all digested, there won't be any left to bind to the repressor protein, so the repressor protein sticks back onto the operator, and stops the transcription.

Answer 2

Get your textbook out and open it and read the section on regulation of gene expression. Pay attention to the section where it discusses the lac operon.