Glucose is the preferable source of energy for E. coli cells. By adding small amounts of glucose, 0.05% in this case, it would enable cell growth to proceed as usual until it has reached mid log growth phase. At this point, the small amount of glucose added should have been depleted and the E.coli cell will now be dependent on lactose present as its source of nutrients. Lactose will also inactivate lac repressors and given the lack of glucose, CAP binding to high amounts of cAMP will be activated and increase expression of lac operon genes.
It should be noted that this system of expression may not tightly regulate the expression of lac operon before the E.Coli reaches exponential phase. As lactose is still present, lac repressors will be inactivated throughout the entire experiment and hence small amounts of proteins might be produced even when not auto-induced. After auto-induction, CAP-cAMP protein complex will simply upregulate expression of lac operon genes.