Lester, 37, will make his final appearance for the Blues on Saturday after the club decided against offering the player a new contract.
With their play-off hopes extinguished last weekend, Chesterfield's last game of the season against the Grecians has nothing riding on it.
Despite that, Cook wants the fans to pack out the Proact Stadium to bid farewell to someone he insists is a club legend.
He said: "Unfortunately we can't look forward to going up, but we can all look forward to a very special day for Jack Lester.
"He will captain the side and will lead us out and I want the ground to be full. I appeal to everyone to fill the ground and make the occasion and the ovation special as he's been a special player for this club.
"I want it to be a special day for Jack Lester and I want all the focus to be on him and his achievements. It will be his day.
"He is a true club legend and I'm sure these supporters will give him the ovation he deserves."
Lester, who joined Chesterfield on a free transfer from Nottingham Forest in the summer of 2007, has scored 92 goals in 218 appearances for the Spireites.