So let's see... I don't want to be indirectly associated with the proceeds of a practice I don't agree with, because I don't want to have to pay for educating my children (that I freely chose to bring into this world) in a private school. Therefore, I would rather take the freedom to buy a lottery ticket away from someone else so I don't benefit from gambling which is what my religious beliefs tell me is immoral.
You tell me which part of this equation more accurately defines what freedom is.
I think you missed the point.
Since it is a government-run lottery (and a monopoly to boot) and the proceeds are specifically designated for school funding, those who do not care to be associated with the operation, either on religious or political grounds, have no escape other than to take their children out of the public schools. Furthermore, the government does not require you, by law, to buy a lottery ticket, but it does require you to send your children to a school recognized by itself.
Finally, it is rather silly to compare your "right" to buy a lottery ticket with your "right" to educate your children in the way you see fit. No one really cares if you gamble. If you really want to, you can zip over to Cherokee or up to Atlantic City. But if the government runs a gambling operation as monopoly and you are completely unable to opt out of the association, the government has impinged on your freedom.
You are arguing convenience against necessity and that boat won't float.