The former England international joined the Villans last month following his release from West Ham United.
Cole has won three Premier League titles and two FA Cups during his career, while also featuring in the Champions League during a loan spell at Lille.
However, Lambert believes that the 32-year-old is "still hungry" to make an impact at Villa Park, despite previous successes.
"As soon as you start to lose the fire from your stomach as a footballer there's no point," the Villa manager is quoted as saying by the Birmingham Mail. "He still wants to do really well and he's still hungry to do really well. That's a sign of a top, top player.
"If you have still got the attributes at that age that you had when you were 16 or 17 starting out, you will not go far wrong. He can make things happen. If he can perform the way I know he can then we have got a really good player on our hands."
Aston Villa kick off their Premier League campaign with a trip to face Stoke City on August 16.