Lamela, 24, has not played since Spurs' 2-1 League Cup defeat at Liverpool on October 25 and spent a week in his native Argentina in December visiting his hospitalised brother.
Despite subsequently returning to London, he has missed Tottenham's run of five successive Premier League wins and Pochettino decided a change of scenery would be beneficial.
"He went to Italy now. They need to change a little about the atmosphere. He has strong links in Rome," Pochettino told a press conference at the Tottenham training centre in north London.
"We hope that after that period he will come again and be available to start training with the team.
"It's always difficult for players who spend a lot of time (out) and with the energy of the team, sometimes he is frustrated he cannot be involved today as it's only him out of the group."
Lamela, who has travelled to Rome with a Tottenham physio, joined Spurs from Roma in a reported £25.7 million ($31.7 million, 30 million euros) deal in 2013.
He spent two years at Roma after making his name with River Plate in his homeland.
"He has a special link with the physios and doctors in Rome, so thank you to Roma for opening the door to him," added Pochettino, whose side beat Premier League leaders Chelsea 2-0 on Wednesday.
Lamela is the only confirmed absentee for Sunday's FA Cup third-round tie at home to second-tier Aston Villa, but Pochettino is expected to rest several first-team players.
Fringe players Vincent Janssen, Kieran Trippier, Ben Davies and Harry Winks are among those in contention to start.
Last year Pochettino vowed to sing a duet with chairman Daniel Levy if Spurs won the FA Cup and he made a similar pledge ahead of this season's tournament.
"It cannot be the same because I think it is bad luck to say if we win we will sing on the pitch with Daniel," he said.
"Maybe we find another challenge, no? Maybe I try to dance. Why not? Anything you ask me, if we win it or the Premier League, I will do in the middle of the pitch, no problem."