I don't know about NY, but if they are like California, then there will be no difference in education funding. In CA, the lottery money simply replaces what the state would have spent on education. If more people buy lottery tickets, then the increased revenues offset the amount CA is obligated to pay for education, thereby freeing more money for our legislature to waste on long-term pork programs.
That is EXACTLY how it works in ALL states.
It's like the UGF pretense that you can DIRECT your contribution to a particular charity. Sure you can...and then they take that amount of money from the general fund that they would have normally given to that charity and put it where ever they choose.
It's all a mirage.