Kozak suffered the injury in training on New Years' Day, a bitter blow for the Czech Republic international, who arrived at Villa Park from Lazio at the start of the season.
But three months on from the incident, Lambert has revealed the striker is now off his crutches and is ready to start the next phase of his rehabilitation.
"Libor is doing great," the Scot told the club's official website. "He is off the crutches now. I think he's in a much happier place within himself now as well.
"The thing with Libor is he's a top boy so you know that, with his rehabilitation, he'll knuckle down.
"He'll not cut any corners. He'll have good days and bad days because of the mental stress of it but he will do his utmost to get fit.
"He's on course, certainly. We're hoping that by pre-season, he'll not be too far away. Libor is definitely doing well.
"He was down when the whole thing happened and for a few weeks after that.
"But I saw him the other day and we were having a chat. I think coming off the crutches has been a major step considering the amount of time he was on them."
