Sales tax has to be calculated carefully to replace the lost tax revenue attributable now to the current taxes. Additionally, the sales tax should be made to be "progressive" – necessities are taxed at 0 or the lowest rates, luxuries at the highest rates. This is an easy exercise.
National lottery is "extra." It pays for the additional obligations we're faced with from social security and Medicare due to the aging population.
And it's mostly financed by old people who spend their social security now on state lotteries and bingo anyway 🙂