The 33-year-old moved to Molineux from Newcastle United on an 18-month contract in January 2016 but almost immediately picked up a hamstring injury that kept him on the sidelines for 14 months.
Williamson has played three games since returning to action and while he has impressed Lambert with his performances, the manager has urged him to continue to demonstrate his worth in the remaining games of the season if he wants a new deal.
"He has to prove his fitness and sustain it. He knows that," Lambert told the Express & Star. "He's not a young player coming through learning the ropes, he knows exactly the game and how he wants to play it and how his body feels.
"Whether he can do half a dozen games in a row I'm not sure, because the length of time he's been out is huge. I think he can get away with one or two games. Whether he can do back-to-back is a big thing for him at the minute after so long out.
"You can get away with him at Reading or Stoke, but the problem is when someone's been out for that length of time you tend to find they get little niggles elsewhere, although his main injury feels good, because the muscle aren't trained. For a footballer not to have a pre-season is a big thing because you're not conditioned."
After being rested for the game at Brentford on Tuesday, Williamson is expected to be back in contention for the trip to Fulham on Saturday.