The 21-year-old suffered a fresh blow on Monday night when being helped off the pitch in the first half of Wanderers' 1-1 draw with Brentford.
It is not yet known exactly how long Clayton faces on the sidelines, but Lennon offered a pessimistic response during his latest press conference when asked about the forward's fitness hopes.
"[Clayton] is seeing a specialist today to see if he'll need surgery. If he does, he'll be out for the season," the Ulsterman told reporters.
Lennon did provide a positive outlook on the club's search for some fresh investment, though, following rumours that Wanderers faced the prospect of being placed into administration within the next 48 hours.
"I've spoken with Trevor Birch and I'm hearing positive things," he added. "Regardless, we'll keep going and focusing on what we can do. I'm like everyone else. I want what's best for the club. Yes, it's a difficult time, but we have to trust the process"
Bolton are currently bottom of the Championship table after winning just one of their opening 18 fixtures this season.