The 13-year-old was planning to expose their relationship, the official said, and investigators believe he stabbed her
to prevent that.
The law enforcement official would not describe the nature of the inappropriate relationship.
Investigators have been tight-lipped about the evidence they have that allegedly ties Eisenhauer to the killing.
Nicole's mother "had tried to stay on top of" her daughter's Internet activity, according to Kenny Jarels, who spent two days with the girl's family between when she was reported missing and the discovery of her body on Saturday.
But the mother, Tammy Weeks, was "not aware of the extent" of what Nicole was doing on social media, said Jarels, who is with the nonprofit group Help Save the Next Girl
which focuses on sensitizing young women and girl to predators.
"She was a good mother," the advocate said of Weeks. "She was very protective of Nicole."
An attorney for Eisenhauer has declined to comment on the case.
Police arrested the 18-year-old college freshman late Friday. He was already facing charges the next morning, before Nicole's body was found.
Police have said he and Nicole were acquainted before her disappearance, and that he "used this relationship to his advantage to abduct and then kill her."
Eisenhauer did not lead authorities to the body, according to Blacksburg police Chief Anthony Wilson, nor did he confess to murder. Still, authorities managed to piece things together after sorting through social media, exploring 300-plus tips and searching for other information pertinent to the case.
A spokesman for Kik, an app that allows users to send anonymous messages, told CNN on Tuesday that it had cooperated with an FBI investigation into the case.
"This involved responding to multiple emergency requests under our Emergency Disclosure Request policy, according to which we release certain account information to law enforcement agencies for cases that involve imminent threat of death, loss of security or serious physical injury to any person," Kik spokesman Rod McCleod said.
If he's convicted of first-degree murder, Eisenhauer faces a sentence of 20 years to life.
His Virginia Tech classmate, 19-year-old Natalie Keepers, faces charges of being an accessory to murder before the fact, concealing a body and being an accessory to murder after the fact.
A hearing in her case is scheduled for Thursday morning. Her attorney has declined to comment.
Funeral services for Lovell
will be held Thursday afternoon.