Lamela, 19, who joined the Giallorossi earlier this summer from River Plate in a 12million euros deal, sustained an ankle injury while competing for Argentina at the FIFA Under-20 World Cup this summer.
Without Lamela, the Eternal City giants got off to a bad start to the season.
Roma failed to qualify for the Europa League group stages after losing 2-1 on aggregate against Slovan Bratislav last month.
Despite the setback, Roma, under new coach Luis Enrique, are optimistic they can start the domestic campaign on a winning note.
"We are looking forward to the start of the season," said Roma captain Francesco Totti.
"I hope this new season hands great satisfaction to our fans.
"We have so many new players in the team and we will all have to get behind our new coach in order to begin in the best possible way."
Former Barcelona striker Bojan is set to make his Serie A debut on Sunday playing alongside Totti in attack.
Rivals Cagliari travel to the Italian capital having suffered a huge blow with midfielder Sebastian Eriksson ruled out until next year.
The Sweden international, who joined Cagliari on loan from IFK Gothenburg this summer, got hurt and underwent surgery this week to repair a torn anterior cruciate ligament in his left knee.
Cagliari coach Massimo Ficcadenti, who replaced Roberto Donadoni last month, will also be without Argentina striker Joaquin Larrivey, who serves a one-match ban on Sunday.