The two pitchers are included on the taxi squad, which allows them to travel with the team, participate in workouts, and be added to the roster as injury replacements.
Clevinger could also miss the entire postseason after questions surrounding his injured arm went unanswered during a bullpen session Tuesday, sources told ESPN's Jeff Passan and Jesse Rogers earlier Wednesday.
The 29-year-old Clevinger was diagnosed with a right elbow posterior impingement on Sept. 25 and received a cortisone shot. San Diego was optimistic he could pitch in the wild-card series.
Clevinger was acquired from the Cleveland Indians at the trade deadline in a blockbuster deal involving nine players.
The Florida native made four starts for San Diego, authoring a 2.84 ERA, 2.35 FIP, and 0.90 WHIP in 19 innings.
Lamet was pulled from his last regular-season start and diagnosed with biceps tendinitis.
The 28-year-old, who missed the entire 2018 season following Tommy John surgery, posted a 2.09 ERA with 93 strikeouts in 69 innings this year.