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.