The 32-year-old midfielder swapped West Ham for Villa Park last month when he agreed to become part of Lambert's new-look set-up.
Precocious as a teenager, Cole has won 56 senior England caps during a career which has taken him from Upton Park via Chelsea, Liverpool and Lille to Villa, but which has run rather dry in recent seasons.
However, Lambert is convinced he still has what it takes to succeed at the highest level.
He said: "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.