Legally speaking, at least in the United States, laws are designed so that people do not benefit from their illegal activity. For instance, a criminal cannot receive proceeds from his story if made into a movie or book (it's more complicated than a one line explanation, of course).
I would have to argue that no, the lottery should not pay out if the money used to pay for the ticket was stolen or received illegally.
Of course, that begs the question - what constitutes illegal proceeds? Obviously, in this case, the woman stole a credit card and then bought something with it. The money wasn't hers, so stolen = no right to lottery winnings. But what about generational theft. Or legal proceeds from ill-gotten funds?