Another profitable industry besides mining could be setting up nursing homes on the moon, where wealthy elderly folks could live fuller lives due to the reduced gravity. Yes, the idea of this only being available to the super-rich (at first) is nauseating to me too, but if it provides the source of funding to establish sustainable moon bases, that would be incredible, and other industries could follow afterwards, including e.g. new sports leagues such as low-gravity basketball and soccer.
Eventually, enough people would be living on the moon as helpers for the wealthy folks and athletes that eventually there would be so many working-class people on the moon that secondary and tertiary industries would spring up to provide products and services for the working-class people. Soon enough it would become profitable to farm crops on the moon (for lunar consumption), build products on the moon (for lunar consumption), and more.
We'd eventually get to the point where a lunar nation could have positive GDP and be economically self-sustaining. It would be a trade partner with the terrestrial nations, and be the first new nation to step beyond Earth. Generations of people will get married and be born there, and humanity would be a step closer to settling the cosmos.