Hernandez's death came just a few days after he was acquitted of most charges in the double murder case.
After his death, doctors found the 27-year-old Hernandez had advanced chronic traumatic encephalopathy, a degenerative brain disease linked to concussions and other head trauma commonplace in the NFL.
Transcripts the Bristol County sheriff released last year of more than 900 jail telephone conversations Hernandez had with family and friends showed he expected to be released from jail and resume his football career shortly after his arrest for Lloyd's killing.
Hernandez had a five-year, US$40 million ($60.6m) deal with the Patriots at the time of his arrest.
McDermott and producer Terry Leonard say the film "examines the perfect storm of factors leading to the trial, conviction, and death of an athlete who seemingly had it all".
Film-makers and authors have had no shortage of material to work with in recounting the story of the handsome, polite athlete from Connecticut, who was a high school standout and an All-American at the University of Florida before his three seasons with New England and subsequent fall from grace.
A state police report of the investigation into Hernandez's death said the player wrote "John 3:16", a reference to a Bible verse, in ink on his forehead and in blood on a cell wall.
And authorities said Hernandez was a member of the Bloods street gang and had been disciplined for having gang paraphernalia in prison.
- AP