A bacterial strain uses both glucose and lactose. When glucose is depleted, lactose metabolism starts after a lag phase.
Bacteria facing mixture of carbon sources implement economical sequential use, a phenomenon first quantified by Jacques Monod in E. coli. In medium containing glucose and lactose, glucose supports faster growth and higher biomass yield, so it is prioritized. During glucose consumption, phosphotransferase component EIIA-Glc remains dephosphorylated, binding and blocking lactose permease LacY via inducer exclusion, preventing intracellular lactose accumulation. Additionally unphosphorylated EIIA inhibits adenylate cyclase, keeping cAMP low, therefore catabolite activator protein CRP remains inactive and cannot enhance lac promoter activity. Lac repressor LacI remains bound to operator, beta-galactosidase LacZ is not synthesized. When glucose exhausts, EIIA becomes phosphorylated, inhibition lifts, cAMP surges, CRP-cAMP complex binds upstream DNA bending it for RNA polymerase, plus allolactose isomer inactivates LacI. A brief lag occurs while LacY and LacZ are synthesized de novo, then second exponential phase proceeds on lactose hydrolyzed to glucose and galactose. This biphasic pattern ensures energy optimization, avoiding costly parallel enzyme production.
Ref: Brock Biology of Microorganisms, 16th ed., Chapter 5: Microbial Metabolism - Diauxic growth and catabolite repression.