Winning the lottery can be a bolt of amazing luck. But whether the luck lasts depends on whether lottery winners fritter away their unexpected largess or manage to achieve financial security.

When Alcario and Carmen Castellano won $141 million in California more than a decade ago, they were fortunate enough to have a financial professional in the family to advise them. And one thing they learned early was to say no, said Mr. Castellano, now 83.

People were constantly calling their San Jose home after they won in 2001, and many even knocked on their door, trying to persuade them to lend or give money. Mr. Castellano said that not long ago, an acquaintance asked for a personal loan. “That’s not our goal,” he quickly told the person. “We don’t do that.”

Within months of winning, the couple had to buy a more secluded house because they did not feel safe. He said, joking, that it was also “because the Jaguar I gave my wife would have looked out of place in our old neighborhood.”