Tierney, 26, was a regular at left-back for the Canaries during the opening months of the season but has been out for almost four months.
He was hoping to make a return for the East Anglian side's finish to an impressive first season back in the Premier League but aggravated his injury when playing for the reserves last Tuesday.
This exacerbation of the injury led to surgery which Lambert admitted had ruled Tierney out for the rest of the campaign.
He said: "Marc Tierney has had operation on his groin injury and will be out until pre-season."
Lambert also revealed that young defender Daniel Ayala would not need surgery after breaking down in the same reserve game as Tierney.
However, the Spanish centre-back will also not feature again for the Norfolk outfit this season.