Cole was snapped up on a free transfer from West Ham United.
Lambert told the Birmingham Mail: "As soon as you start to lose the fire from your stomach as a footballer, there's no point.
"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.
Lambert added: "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."
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