Question

Using your knowledge of activators and repressors, hypothesize two ways in which transcription of the lct gene could be turned off.

Answer 1

One hypothesis would be that there are allosteric repressors that bind to RNA-polymerase and change its conformation. This way, it's unable to bind to the promoter for lct gene.
Another hypothesis would be that the repressors bind to a silencer or operator sequence of the lct gene. This prevents transcription of the gene even though the RNA polymerase may be capable of binding to the promoter.