She appeared some 30 hours later with injuries on her face and claimed she had been kidnapped and raped by men of North African or Middle Eastern appearance.
The claims were explosive in the wake of the Cologne sex attacks, and saw protests by the Russian-German community and the Pegida anti-Islam movement.
Police said there was no evidence of rape but refused to comment further to protect the girl's privacy as a minor.
Russian media seized on the case, alleging a cover-up.
"The news of her disappearance was kept secret," Lavrov told a press conference.
"They are painting over reality with political correctness."
Russian television reports were riddled with bizarre inaccuracies, including footage of what appeared to be Swedish police.
Prosecutors finally broke their silence over the case after the girl's mother gave an interview to Spiegel magazine.
She had admitted the rape allegations were a lie when she was questioned three days after her disappearance, Martin Steltner, a spokesman for proscutors, said.
"She immediately admitted the rape story was not true," he said.
It now appears Lisa went to stay with a 19-year-old acquaintance because she was scared to go home after her school contacted her parents over unspecified problems.
She made up the story to explain her disappearance.
Police say no sexual contact took place, either consensual or non-consensual, and the 19-year-old is not under any suspicion.
"My daughter is doing badly," her mother told Spiegel. She is currently undergoing psychiatric treatment in hospital.
