Lee was born Thomas Lee Bass on October 3, 1962, in Athens, Greece, to father David Lee Thomas Bass, an American U.S. Army sergeant, and mother Vassilikki "Voula" Papadimitriou (Greek: Βασιλική Παπαδημητρίου), a Miss Greece contestant for the 1960 Miss World event. His family moved to California a year after he was born. He received his first drum when he was four years old, and his first drum kit when he was a teenager. Lee dropped out of high school to pursue a career in music, starting with the band Suite 19. He has a younger sister, Athena Lee (née Bass), who was also the drummer in his solo band KrunK and was married to James Kottak, the drummer for the rock band Scorpions.

As a teenager, Lee listened to Led Zeppelin, Van Halen, Cheap Trick, Kiss, AC/DC and Sweet. His main drumming influences were John Bonham, Tommy Aldridge, Alex Van Halen and Terry Bozzio.