Geauga County Prosecutor David Joyce said Lane admitted he brought a .22-caliber pistol and a knife into the building.
"He chose them randomly," Joyce told The (Cleveland) Plain Dealer, adding Lane allegedly fired 10 shots inside the school's cafeteria before being chased away by two school officials.
Lane, a 17-year-old sophomore, was handcuffed and wore a bulletproof vest when he was brought into the courthouse by several police officers. His grandfather and two aunts were in the courtroom when he told Judge Timothy Grendell he understood his right to remain silent, the newspaper said.
Lane is to remain in the Portage-Geauga Juvenile Detention Center in Ravenna for now. Prosecutors, who are expected to charge him as an adult, have until Thursday afternoon to file charges and the judge set further hearings for March 6 and 19, the newspaper said.
The judge also set a hearing for Wednesday on a request from the media to see any juvenile records related to Lane, his family and one of the victims.
Three students have died of gunshot wounds sustained when a teenage gunman opened fire on students sitting at a table in the school cafeteria. Two other students were wounded, with one still hospitalized Tuesday.
While officials said Lane didn't know his victims, one student grazed by a bullet said he knew the suspect in middle school and the newspaper said several of those shot rode a bus with Lane each day and were listed as friends on his Facebook page.
Joyce said Lane was "not well" and there was no evidence bullying or drugs were involved.
CBS News reported a hospital statement said Demetrius Hewlin, a student from Chardon High School previously listed in critical condition, had died.
His family issued the following statement: "We are very saddened by the loss of our son and others in our Chardon community. Demetrius was a happy young man who loved life and his family and friends. We will miss him very much but we are proud that he will be able to help others through organ donation. We ask that you respect our privacy during this difficult time."
Though it did not give the victim's age, a report in The Plain Dealer said he was a junior.
Hewlin's death was reported shortly after another student, Russell King Jr., 17, was declared brain dead.
A spokesman for the Cuyahoga County Medical Examiner's Office said the "cause and manner of death of this case are under ongoing investigation and will be released upon completion."
Hospital officials said King was pronounced brain dead Monday at MetroHealth Medical Center in Cleveland and the Cuyahoga County Medical Examiner's office was notified, The Plain Dealer reported.
Also killed was Daniel Parmentor, 16.
The wounded students are Joy Rickers, 18, a senior, and Nick Walczak, 17, a junior, officials said. Rickers has been released from a hospital.
The suspected shooter was arrested after he was chased out of the school by a teacher. Police said the teen turned himself in to two bystanders on the street.
Attorney Bob Farinacci, speaking for Lane's family, told WKYC-TV, Cleveland, Monday the 17-year-old was "extremely remorseful."
"He's very confused. He is very upset," Farinacci said. "This is a very scary circumstance that I don't think he could have possibly even foreseen himself in the middle of."