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Superman is weakened instantly by a block of kryptonite the size of my fist, even when it is ten feet away. He is helpless. And when it is placed around his neck, he can't even move.
So, let's say that in that scene, Bellatrix walks up on Superman while he is helpless in the pool and death spells him. What happens?
I'll tell ya. Death.
And since Supes Returns is the same character, since it is Canon, it is safe to say that when Bellatrix apparates ten feet from him with kryptonite, he will be helpless.
And yes, Luthor would definitely give them kryptonite to weaken Superman.