One of LSU's best players had the same situation, Chris Jackson. He actually waited till he was of age(18?) to sign another LOI that his mother did not need to sign.
Actually I was wrong about Jackson. He never signed the LOI, which I guess is the only thing that needs to be signed my a parent. He just enrolled at LSU w/o one as he didn't need his mother's consent to receive the schollarship. My bad.
You don't have to sign a LOI at all...so the deadline is essentially enrollment day at LSU. Someone on another board said the effective date is the clearinghouse.