I prefer the government run, they own everything here, all they need are people who are honest and transparent, it's a good source of revenue for the government, instead of a private company making millions, they can use that million to add revenue to fund the government projects, in the Philippines they funded many hospital and charity homes, so it should stay in the government.
It's hard to find an honest employee if the law is not so strict against people who are corrupt in service.
Everything should start with a law and impose it strictly and for sure that will create an honest employees.
When Lottery is run by private institution, there's a chance that they would not be able to remit the correct tax.
Also, I don't think lottery will be given to the private when this business has no risk for operators, they just have to facilitate the game and pay the winners out from a certain percentage of the total collection, that's an easy money.