Why does the lac operon shut down some time after the addition of lactose in the medium where E.coil was growing ? Why low level expression of lac operon is always required ?

Explanation

After addition of lactose, complete breakdown of lactose to glucose and galactose\takes place. Therefore, there is no more lactose to bind to repressor protein and the lac operon shut down. A very low. level of expression of lac operon has to be present in the cell all the time, otherwise lactose cannot enter the cells.