Final answer:
A mutation in the lacI gene that increases the affinity of the lac repressor for allolactose would lead to increased expression of the lac operon.
Step-by-step explanation:
If a mutation in the lacI gene increases the affinity of the lac repressor for allolactose, it would result in the repressor binding to allolactose more readily. This means that the repressor would be more likely to release from the operator site of the lac operon, thus de-repressing it. Consequently, there would be an increase in the expression of the lac operon, as the presence of allolactose signals that lactose is available for metabolism, and the repressor should not block the transcription of genes responsible for lactose metabolism.