NEW YORK—DoorDash Inc. sued New York City on Wednesday over a new law requiring food delivery companies to share customer data with restaurants, saying it violates customer privacy and lets restaurants compete unfairly. The lawsuit is the latest battle in a series of legal clashes between food delivery app companies and cities. It was filed in federal court in Manhattan six days after DoorDash, Grubhub Inc., and Uber Eats sued the country’s most populous city over a separate law capping fees that delivery companies charge restaurants. “The law puts consumers first,” Nicholas Paolucci, a spokesman for the city’s law department, said in an email. “It puts them in control of their information when they place orders through these apps.” New York City has tried since the coronavirus pandemic began to help restaurants that had complained about food delivery app fees as high as 30 percent, but which became more dependent …