The chances of KL pulling the codeshare off the INV to replace it with a LPL codeshare are somewhere between slim and none. INV and SOU are both airports that are at least 2 hours drive from the next nearest airport served by KL. Both airports compliment KL's existing network as they don't really compete with any airport already served by KL .
Not Southampton, it's about an hour's drive from KL at Heathrow-4.