Temporary good fortune. Several times one had good success. ‘Run’ implies consecutive steps of luck. It also can be used as ‘ run out of luck’ that is, it comes to an end. (Compare to On a roll.)

“It is said the founder of Fed Ex in the early years ran out of money and took his last payroll to gamble in Las Vegas and fortunately he had a run of luck and made enough money to keep the business going onto its ultimate success.”