Investigators were at a loss to offer a motive for the shooting spree that broke out in the quiet community about 30 miles (48 km) south of Charlotte, North Carolina.
“We have probably more questions than you do right now,” Tolson told reporters at a briefing.
There was no indication that Adams had any relationship with Lesslie or his family, Tolson said.
The sheriff said two weapons were used in the violence, a .45-caliber and 9mm weapon.
Adams died from a single gunshot to the head at his home a short distance from the murder scene, where he lived with his father, as police closed in hours after the shootings, officials said.
As a player, Adams had a six-year NFL career as a defensive back with five teams, finishing with the Atlanta Falcons in 2015. He attended South Carolina State University and was selected in the seventh round of the 2010 draft by the San Francisco 49ers.
Adams’ father, Alonzo Adams, blamed the shooting outburst on football.
“I can say he’s a good kid,” the elder Adams told WCNC-TV in Charlotte, North Carolina. “I think the football messed him up.”
Asked to comment, an NFL spokesman said, “Our hearts go out to the families and friends of the victims of this devastating tragedy.”
The deadly shooting spree, reported late Wednesday afternoon, left a trail of bodies around the Lesslie home. Killed were Lesslie, 70, his wife Barbara Lesslie, 69, two of their grandchildren, 9-year-old Adah Lesslie and 5-year-old Noah Lesslie, and James Lewis, 38, an air conditioning technician working at the house, the sheriff’s office said.
A sixth victim, also an air conditioning technician, was wounded and rushed to a hospital, officials said. He remains in critical condition, the sheriff said.
Robert Lesslie, whose online biography said he co-owned two local urgent care clinics, was a beloved member of the community, Tolson said.
“Dr. Lesslie was a healer in this community,” he said. “He knew everyone. He treated everyone with respect.”
He also had worked in and directed several busy emergency rooms at Charlotte-area hospitals and had been medical director of the emergency department at Rock Hill General Hospital for almost 15 years, the biography said.