The WOPR computer called Lightman back, and the government most likely looked up the residence associated with Lightman's landline. Once the government found his address, they staked him out and kidnapped him. They had more data on him as well, as one of the individuals working at NORAD said: "He does fit the profile perfectly: he's intelligent, but an underachiever, [is] alienated from his parents, [and he] has few friends... A classic case for recruitment by the Soviets." (55:30) [1]
David Lightman is apprehended by the FBI.
According to the New York Times, Ronald Reagan watched WarGames, then asked one of the senior generals if something such as the hacking of the NORAD computer in WarGames could actually happen; the general told him: "Mr. President, ... the problem is much worse than you think." This can be related to the misuses of government databases, specifically the FBI National Crime Information Center (NCIC), and how this database has been accessed illegally in the past by particular individuals with clearance, for the purpose of investigating acquaintances or potential employees. [2]
Lightman accessing the professor's location data.
Despite the Professor changing his name, David Lightman figured out where he was located by using the computer in one of NORAD's rooms. In terms of privacy, the Government did not have any of this data protected from unauthorized users - specifically the Thermo-Nuclear War Program and the data concerning the professor - so they were wide open to an attack by simply combing through the data on the computer. (1:02:39) [1]
[1] YouTube, WarGames, 6 Jan. 2020, www.youtube.com/watch?v=HNLQ-O-Qx3Y&t=1779s&ab_channel=YouTubeMovies (20 Sept. 2021)
[2] Fred Kaplan, ‘WarGames’ and Cybersecurity’s Debt to a Hollywood Hack, (New York Times, 19 Feb. 2016), https://www.nytimes.com/2016/02/21/movies/wargames-and-cybersecuritys-debt-to-a-hollywood-hack.html (20 Sept. 2021)