The 21-year-old, who signed for Spurs from Roma for a record £30million fee last summer, sustained the injury as the result of overcompensating for a previous thigh problem.
The Argentina international has seen a specialist abroad for treatment and recently returned to north London as he works to get fit to take part in the season run in.
The Argentinian, who is considered by many to be one of the most promising youngsters in world football, has struggled to settle at White Hart Lane but has moved his family to England and is determined to learn the language.
He has made just three starts in the Premier League and only 17 appearances in all competitions, scoring a solitary goal in the 2-1 Europa League win over Tromso last November.
Manager Tim Sherwood said on Wednesday he is cautiously optimistic over Lamela's return before the end of the season.
"He's back now at the training ground. He's having rehab. It's slowly, slowly, he's getting closer, as you would expect," he said on Wednesday.
"There was a problem with his thigh, then they diagnosed the problem with his back. He is having continued treatment and now he's started rehab.
"We're hoping to have him back before the end of the season but there are no guarantees."