A Florida police spokeswoman cited the court document Tuesday.
The conversations allegedly involved two people who were with Hernandez when he picked up Lloyd from his Boston apartment early on June 17, hours before a jogger found Lloyd's body in a North Attleborough, Massachusetts, industrial park. All three men are now in custody.
Prosecutors accuse Hernandez, a standout tight end whom the New England Patriots cut soon after his June 26 arrest, of orchestrating Lloyd's death. The 23-year-old is now in a Massachusetts jail; he has pleaded not guilty to murder charges.
The information in a document filed in Florida -- as detailed by Miramar, Florida, police spokeswoman Tania Rues -- may help authorities as they build their case against Hernandez as the triggerman.
Nearly 1,500 miles from the crime scene, Miramar is where Ernest Wallace turned himself into authorities on June 28 after seeing news reports that an arrest warrant had been issued for him. He was charged the next day with being an accessory after the fact of murder.
The other man arrested in the case -- Carlos Ortiz, who hails from Hernandez's hometown of Bristol, Connecticut -- told authorities that Wallace told him Hernandez fired the shots that killed Lloyd, the document cited by the Miramar police spokeswoman says. The document was part of a search warrant executed at a Wallace family home.
This detail comes out the same day that, following a judge's orders, Massachusetts authorities released a number of documents pertaining to the 27-year-old Lloyd's death.
Among other details, these documents explain authorities' account of an interaction with Hernandez at his southeast Massachusetts home after Lloyd's death but before the football player's arrest.
Hernandez at one point told police that he didn't remember specifically when he last saw Lloyd. Later in the conversation, he "became argumentative" with two police officers questioning him, then went in his home and got a business card for his lawyer to give to them.
"We informed Mr. Hernandez that this was a death investigation," the document states. "Mr. Hernandez slammed the door and relocked it behind him.
"Mr. Hernandez did not ask the officers whose death was being investigated. Mr. Hernandez's demeanor did not indicate any concern for the death of any person."
By contrast, when police first told Hernandez's fiancee about the death of Lloyd, who her sister was dating, "she immediately began to cry."
According to the same court document, the same woman told authorities that she and Hernandez went out to dinner for Father's Day, then she went to bed while her fiance was out all night.
Police say that, at one point, Hernandez called the woman and told her "his sports agent said she should not speak with us and that she should request to speak with her attorney," a document states.
Documents also reveal details, some of them previously disclosed, of Lloyd's texts on the day he was killed. One of them, sent at 12:22 a.m. on June 17 to Hernandez's cell phone, reads: "We still on."
About three hours later, a man who works at NeedleTech -- a medical device manufacturer with a facility in North Attleborough, near where Lloyd's body was found -- told police he was taking a break in his car when he heard "three gunshots and (a) car door slamming."
A different affidavit for a search warrant features three black-and-white photos from a home surveillance camera that show Hernandez and two other men.
The three men leave the garage of the North Attleborough home around 1 a.m., the document states. The video shows them returning to the same residence around 3:26 a.m., including Hernandez going to-and-from the basement on "several different occasions."
CNN's Greg Botelho contributed to this report.