Lee was Wales' starting tight-head for the first two Tests against the All Blacks this summer before coming on as a replacement for Tomas Francis in the third.
Despite strong Welsh starts in the first two encounters, Lee and company could not convert them into wins and finished the tour on the end of a 3-0 series defeat.
Now the 23-year-old, who appeared ten times in the Guinness Pro12 last year as Scarlets finished just outside the play-off places in fifth, faces time on the sidelines.
"Samson has undergone shoulder surgery and is expected to be unavailable for 12-16 weeks," said Scarlets physiotherapist Matthew Rees.
But there was positive injury news for Scarlets elsewhere with DTH van der Merwe, Emyr Phillips and Gareth Owen all on target for the season opener.
"We're pleased to see DTH, Emyr and Gareth making good progress and on track to be back in action for the start of the season," Rees added.
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