It seems fairly obvious that competition among private-sector lotteries would tend to increase the payout-to-price ratio. That seems like a fairly clear consumer harm from a state monopoly. As for the government’s getting the money from another source: That’s not the way conservatives usually look at the creation of new revenue streams. When a state without an income tax proposes to create one, we don’t say, Oh well, if we don’t go along with this they’ll just raise property taxes. And we’re right not to view it this way. Revenue should be raised in a way that forces governmental restraint. Having a bunch of little revenue streams, rather than one large tax, makes it easier for government to grow. That’s especially true when a revenue stream is not felt as an exaction by the payer.
To put it another way: I like taxes that generate tax revolts from time to time. That’s why I’d prefer state governments rely on property taxes rather than sales taxes. And it’s why state lotteries seem like an especially bad idea.