It comes from the same source as the scaremongering in Florida before the lottery was introduced there. First of all, they extended the lottery to "approval of casino gaming" which was nonsense. In any event, the people who control casino gaming have a vested interest in keeping non-organized, street crime down...it drives away tourists. In Las Vegas forty years ago it was worth your life to commit a street robbery. Don't worry about the cops; worry about Tony Soprano's boys taking you on a ride to the desert.
The lottery doesn't lend itself to enhanced criminal activity; if someone is going to rob a 7-11 they'll do it with or without a lottery. Lottery tickets are simply convenient items of value to steal if you're a particularly stupid crook. The real opportunity for crime occurs at much higher levels, where there is a serious temptation to siphon off money for something other than what the lottery was intended.