Neesham, who was bought at this year's auction, and Lynn retained from last year have both been ruled out based on the injury reports received from their respective boards, said a BCCI release.
IPL regulations permit replacement if a player is unavailable for the entire season.
KKR have opted to replace the injured players with the experienced duo of Azhar Mahmood, former Pakistan Test Cricketer who is currently based in England playing for Surrey and Johan Botha, former Proteas captain and currently playing for Adelaide Strikers at the Big Bash.