There is little doubt that the British were aware of the likelihood that the Lusitania would be sunk and that it would be the catalyst to bring the US into WWI and Churchill was almost certainly aware of this due to his position in the government. However, to accuse him of being "behind" the sinking implies that he assisted the Germans in doing this and that would be treason -- and that is an outrageous accusation.
Their intention was to violate American neutrality.