In addition to routinely referring to stoic head coach Bill Belichick as 'Daddy,' Hernandez irked Brady by wearing flip flops during a walk-through practice.
At that point, according to Lloyd, Brady had seen enough.
'He was out at the walk-through in flip-flops trying to run around,' Lloyd said. 'He was laughing. He was loud. And Tom keeps it serious in the walk-through. And Tom says, 'Shut the f*** up. Get the f*** out of here."'
Brady had previously told Hernandez's old University of Florida Gators teammate Tim Tebow that he was looking out for his new teammate but he was 'a lot to handle'.
However it seemed even the legendary player had had enough of Hernandez's antics by that point.
After Brady snapped, Lloyd said Hernandez went from laughing to boiling over with rage.
'It was like he went from this child-like, laughing, disruptive behavior… and he storms off in a fit of rage,' he added.
On one occasion, Hernandez did get Belichick to indulge his childlike behavior. Hernandez was complaining about a sore elbow, and Belichick, a father himself, lifted his player's arm and kissed the ailing joint.
'I had a little bruise on my elbow and was whining about it. [Belichick] was just showing me the love of a father figure and he gave me a kiss on the elbow,' Hernandez told a Globe reporter at the time. 'No, I didn't ask him. I damn sure liked it though. Felt some love.'
His teammates dealt with his erratic behavior for three years.
On another occasion at training camp, Lloyd recalled veteran receiver Wes Welker telling him to ignore Hernandez's antics.
'He says, "I just want to warn you that [Hernandez] is going to talk about being bathed by his mother. He's going to have his genitalia out in front of you while you're sitting on your stool. He's going to talk about gay sex. Just do your best to ignore it. Even walk away."' Lloyd said of his conversation with Welker.
'There would be swings where he'd be the most hyper-masculine, aggressive individual in the room, where he'd be ready to fight somebody in fits of rage.
'Or he'd be the most sensitive person in the room, talking about cuddling with his mother. Or he'd ask me, "Do you think I'm good enough to play?"'
His problems may have stemmed from a combination of a tough upbringing, drug use and the effects of brutal collisions on the field.
Hernandez's brother revealed that their father would often beat them.
The Globe reports that he hired his high school marijuana dealer, Alexander Bradley, as a paid assistant to calm him down when he burst into fits of laughter, anger or paranoia.
As well as allegedly being Hernandez's drug connection (a New York nightclub worker he briefly dated spoke to the publication about seeing him use cocaine and weed) Bradley later got the Connecticut native a $375 silver revolver.
Hernandez said in an interview the Patriots' way changed him. However he still maintained an apartment filled with weapons and narcotics, which he referred to as his 'side place' according to a friend.
After Hernandez's death, his family donated his brain to Boston University, which found he suffered from the most severe case of Chronic Traumatic Encephalopathy (CTE) – repeated trauma to the brain - ever found in someone his age.
CTE and other afflictions connected to head trauma are major concerns with former NFL players at the moment.
Boston University found that of the 111 brains of deceased professional football players they examined, 110 had some degree of CTE.
The NFL is currently paying out over $1 billion to former players as part of a class-action settlement against the league.
Curiously, Hernandez had only one official concussion during his time in New England, and he still managed to play the following week. In fact, Hernandez even practiced, although he was considered 'limited,' ahead of the next game, a playoff win over the Baltimore Ravens in January of 2012.
The Globe reports Hernandez – who began playing youth football at eight years old- also maintained that he was fine at the time adding: 'I just do what the coaches ask.'
Even starting a family aged 23 with his high school sweetheart Shayanna Jenkins couldn't save Hernandez, according to Patriots linebacker Dane Fletcher.
His daughter Avielle was born on his November 6 birthday in 2012.
'Now he's actually working for something and playing for something, not just himself, because I knew he was selfish,' Fletcher recalls was his thinking.
The New England Patriots player took his own life in April 2017, aged 27, two days after he was outed on The Kirk & Callahan Show, and five days after he was convicted of a double murder.
Hernandez was found guilty of murdering Odin Lloyd in 2015.