If GL were to die in the near future, Howard Roffman is your interrum CEO.

http://en.wikipedia.org/wiki/Howard_Roffman

He's been there since the beginning, has worked up the system understands how to keep it going. But he's not a creative output person. People might transfer GL's creativity into his kids, but beyond Katie's writing there are few signs of the kids keeping the LFL alive. I would guess it massively shrink and like some of his other funds, the name could be used to endorse up and coming film creators. This way the LFL earned moneys go back into the continuation of film making.