What environmental factor causes the lac operon to turn on?

In the lac operon model, lactose acts as in inducer molecule. In the presence of lactose, the molecule binds to the repressor protein. This repressor-lactose complex is unable to bind to the promoter.

When the promoter is not occupied, RNA pol - II binds to it and begins transcribing the structural genes located downstream. Thus, the lac operon is turned on in the presence of lactose.