Mutation of LacZ gene and Allolactose

Mutation of LacZ gene can result in a non-functional beta-galactosidase.
Beta-galactosidase can engage in two pathways. One to lyse lactose to glucose and galactose and the other to convert lactose to allolactose. Allolactose is indeed an isomer of lactose but its presence needs the working of beta-galactosidase aka does not occur naturally.
Thus with a mutated beta-galacosidase, no allolactose can be formed. repressor proteins cannot be removed from operator. No structural genes in lac operon will be transcribed.

FYI: Permease is a membrane bound protein that facilitate the movement of lactose into the bacteria. If the LacY gene is mutated and a non-functional permease is expressed, no lactose will enter the cell and thus no allolactose can be formed as well.