Regardless of your feelings on this specific issue, it’s fair to say we can have two problems at once, and one doesn’t diminish the other.

I don’t think the government should be in the lottery business.

The argument in favor of this generally goes: if there wasn't a government lottery, there would be privately-run lotteries, and attempts to ban lotteries would just push them into the hands of organized crime. At least a government-run lottery will publish honest odds and pay out to winners, which private/criminal lotteries would less reliably do, and that minimizes the harm done by the lottery.

You can apply basically this argument to similar things which the government doesn't do and people typically don't support (like running casinos or selling drugs), though.

They do sell drugs in Canada now, and it seems to be going quite well, actually. Maybe there's a case to be made after all, although, personally, I prefer the Portuguese model of decriminalizing everything.