Especially in the 1950s, the financial transactions of casinos were kind of strange because of how much illicit, off the books mob money was being made. Development of casinos was really hard for mob figures when you have such shady income, lenders do not want to get involved and you really aren't paying for multi-million dollar construction projects in small bills.

I can't say what exactly the motivations of the Mormons were for funding these casinos but you can see how lucrative the loans were for them. Mormons can provide the professional, business side of the casinos, they have access to funds and seem more legitimate than many of the clearly mob related owners.

Later you have the mega rich investors like Howard Hughes who can really bankroll casinos without mob involvement, but he still relies on a group of people who really know the town much better than he does, many of them are LDS and connected to the previous funding.

Casinos eventually become much less shady both in terms of activities conducted there and the ownership. Mormons were willing to deal with the less than legal elements of Las Vegas, assuming risk others wouldn't but getting a good return on investment