Injury update: Benteke staying upbeat despite World Cup blow
Benteke is back in his native Belgium following surgery on the injury which has ruled him out of this summer's World Cup.
The 23-year-old striker's mood is said to be much more positive now he has had time to come to terms with missing the showpiece in Brazil.
And boss Lambert is looking forward to welcoming Benteke back to Villa's Bodymoor Heath HQ in July to continue his recuperation.
"He is in a better place than he was a few weeks ago," said Lambert.
"Now he has got over that hurdle and is a bit more positive.
"We expect him back when everyone comes back for pre-season.
"He will go through the rehab phase of trying to get fit again.
"As I said before, the achilles injury is not a nice one to get. You need to put the work in, which I am pretty sure he will.
"He has been a major miss, no two ways about it. So too has Kozak.
"That's two strikers out with long-term injuries. Losing them has been a major blow."
Meanwhile, Joe Bennett remains a doubt for Saturday's clash against Hull.
The former Middlesbrough full-back is still struggling with the ankle problem that kept him out of last weekend's trip to Swansea.
But defensive colleague Jores Okore has made a big step to reaching full fitness by joining in training with the club's development squad.
"Everyone seems fine at the moment," added the manager.
"But Joe is a doubt. He hurt his ankle from last week. But everyone from the Swansea game is okay."