The 24-year-old, who scored four goals in 14 starts before picking up the injury, broke his leg while training in January.
"Libor is doing great. He is off the crutches now. I think he's in a much happier place within himself now as well," Lambert is quoted as saying by the club's official website.
"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. I think coming off the crutches has been a major step considering the amount of time he was on them."
Kozak joined Villa from Lazio in September 2013 on a four-year deal.