The 22-year-old ruptured his Achilles tendon in Wales win over Ireland at the weekend and will go under the knife next week.
It means Scarlets must make do without Lee in their front row for their final five matches of the GUINNESS PRO12 season, beginning with the visit of Edinburgh Rugby to Parc y Scarlets later this month.
And Gatland also fears Lee's injury could see him miss the World Cup this autumn.
"It's going to be long-term. It could potentially keep him out of the World Cup," said Gatland.
"That's a six-month injury. He was going to be operated on yesterday, but he's got too much swelling, so they are waiting until next week, which unfortunately puts him back a week."
Scarlets, currently seventh in the GUINNESS PRO12 table, are pushing hard for a top-six finish to ensure European qualification for the 2015/16 season.
Following their home game with Edinburgh, Scarlets travel to Zebre and Newport Gwent Dragons, before staging their final home game of the season against Cardiff and finish in Treviso.
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