Cole arrived at Villa Park as a free agent at the start of the season but the 32-year-old only made his first appearance against Everton last week.
The former England international came off the bench for the final nine minutes in Villa's 3-0 Premier League loss to Everton and, while Cole still has "got a bit to go", Lambert says he is close to making a significant impact at the club.
"If we keep Joe fit and up to speed then hopefully it will benefit him and us," Lambert told the Birmingham Mail.
"I think it was justified to put him on the bench against Everton because he's been working really hard.
"His attitude towards football is great and you're talking about a guy who has won things.
"He does everything right. He's a top pro. He doesn't cut corners.
"He's excellent in training, he works hard and he does the extra things that you need.
"You always see that with lads who have won things, though. They know how to do everything and how to do it right."
Lambert added: "I know in my own head where I think his strongest point is.
"I think he will definitely contribute, that's for sure. Overall he's been great.
"He wants to make an impact, he wants to play and that's what you want.
"He's got great enthusiasm for the game."
Villa are away to cellar-dwelling QPR on Monday.
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