Actually, if I recall correctly, most - if not all - states do not collect income taxes on the lottery winnings themselves. Obviously if you invest it, the gains are taxed, but not the principal.
Not in Mass. They will take every nickel up front.
Most states do collect state income taxes, but some do not, notably CA, FL, PA, and TX. Federal income taxes always apply.
The lottery withholding does not usually cover the entire tax bill.