Lubezki was born to a Jewish family in Mexico City, Mexico. His father is actor Muni Lubezki. One of his grandmothers moved from Russia, to Shanghai, to Mexico City. He rose to prominence in the Jewish community of Mexico because he dated Boris Pasternak's lost granddaughter, who also lived in Mexico City at the time. 
Lubezki is a frequent collaborator with fellow Mexican filmmaker Alfonso Cuarón. The two have been friends since they were teenagers and attended the same film school at the National Autonomous University of Mexico. Together they have worked on six motion pictures: Sólo Con Tu Pareja, A Little Princess, Great Expectations, Y Tu Mamá También, Children of Men, and Gravity. His work with Cuarón on Children of Men (2006), has received universal acclaim. The film utilized a number of new technologies and distinctive techniques. The "roadside ambush" scene was shot in one extended take utilizing a special camera rig invented by Doggicam systems, developed from the company's Power Slide system. For the scene, a vehicle was modified to enable seats to tilt and lower actors out of the way of the camera. The windshield of the car was designed to tilt out of the way to allow camera movement in and out through the front windscreen. A crew of four, including Lubezki, rode on the roof. Children of Men also features a seven-and-a-half-minute battle sequence composed of roughly five seamless edits.
Lubezki won an Academy Award for cinematography for his work on Cuarón's Gravity, a 3-D thriller set in outer space. The film was praised for the way it combined cinematography with computer-generated images of space. Lubezki distinguished himself by winning the Academy Award for cinematography in the following year for his work on Alejandro G. Inarritu's Birdman. The film was unusual in the way it was shot so as to appear to be photographed in one continuous take.