genetics - Lac operon: How can lactose enter the cell in the absence of lactose permease?

My textbook states that

lactose permease...transports lactose into the cell

and

When lactose is added to the growth medium, the lactose molecules bind to the other site on the repressor protein

My question is, how can lactose enter the cell to bind to the repressor protein to allow beta galactosidase and lactose permease to be synthesised if there is no lactose permease present to transport the lactose into the cell?

Answer

Introductory textbooks will not get into the details of the lac operon.

Basically, the operon is expressed constitutively at a low level that means that Beta Galactosidase and Lactose Permease are expressed at low levels by the bacterium. This is because it takes a little bit of time to build up the concentration of LacI in the cell before it can start to bind the operator.

The LacI repressor only binds the operator in the absence of Lactose in the cell's environment due to the fact that allolactose allosterically binds the LacI repressor and affects that molecule's ability to bind the operator. So RNA polymerase can bind the promoter of the Lac operon at some low rate and continue to produce the protein.

When the cell no longer has glucose, it generates cyclic AMP, which induces the CAP protein to bind to the CAP site, just upstream of the promoter of the Lac Operon. CAP associates with RNA Polymerase, and this makes the promoter very active. Beta Galactosidase and Lactose Permease levels increase rapidly.

Where you see the full effects of the LacI repressor is when neither Glucose nor Lactose are present in the environment of the cell. At this point the repressor binds to the operator and blocks transcription by DNA Polymerase.

I hope this helps. I have an entire book that covers the Lac Operon, so even though this is a bit expanded of an explanation from a basic textbook, it is still a summary.