The Lexington Avenue subway line will be completely shut down below Grand Central Terminal for four nights starting Monday as the Metropolitan Transportation Authority embarks on a new maintenance strategy aimed at getting crucial work done quickly instead of across a period of months.

The 4, 5 and 6 trains won't run between Grand Central and Atlantic Avenue in Brooklyn between 10 p.m. and 5 a.m. until Friday night. The MTA says riders who would normally take those trains can use other subway lines a few avenues away or ride...