a state saying only we offer lotteries
If we're thinking of taxation as theft, then this should be clear. Prohibiting people from making voluntary transactions under threat of violence is a different type of crime than theft.
By the way, though, I do think it's not as bad to tax luxury/vice items like alcohol. To me the more avoidable a tax is the less evil it is.
The more we go back and forth on this, though, the less I want to be defending the position I initially staked out. Even if the lottery isn't exactly a tax, the state has no right to be conducting a lottery and is only able to do so because it's violently suppressing competition.