Three operations have failed to clear up the groin problem which first affected Dunne during the Republic of Ireland's Euro 2012 campaign.
The centre-half - out of contract this summer - has not played a minute for Aston Villa under Lambert.
But the Villa boss said: "Is it career-threatening? No, nothing like that. You can't say that.
"Richard has been trying his utmost to get back fit. He's been to the best people on the other side of the world.
"He feels good at some points, but not so good at other times. He can't play through the pain barrier with that injury.
"It's been really complicated that injury. Richard has been over to the United States a couple of times to try and get it sorted.
"But there are little niggles that aren't clearing up. That's a real frustrating thing for him."