I read your second sentence but I don't get it. Isn't generating profit for the state literally the entire point of the lottery? Who is arguing that it doesn't do that in theory or practice?
Profit motive implies profit maximization behavior or mandates. A state-run lottery should not have that. Again, in theory.
Profit motive implies profit maximization behavior or mandates. A state-run lottery should not have that. Again, in theory.