Is it legal to purchase and win US lottery tickets online?

I am assuming you mean that you are purchasing a lottery ticket on-line for a state sanctioned and legal lottery that allows so. Problem is, most states do not allow you to purchase tickets on-line at the present moment and I am not sure that I would trust those sites that allow you to "order them".  

As for the legalities because you live in a state that does not allow the lottery, you can purchase lottery tickets from a state with a lottery even though Hawaii does not have one.  It would be no different than you being in New York for a holiday and purchasing one.  The different in this scenario and your is, however, your purchase was in person and through a legal dealer.  It is the dealer from whom you would purchase on line that is the problem.  They may not be sanctioned as legal.