Are all false answers lies? If I tell you "you're going to do X" it's less a statement of fact than a prediction. So if upon hearing these words you proceed to do Y instead of X, even though my statement was false, it's not that I've lied so much as that I was merely incorrect, especially since the chief factor in the outcome of my prediction is your behavior and not my own.
Oscar's threat only covers the conditions that Larry's statement is (a) true or (b) dishonest; he is silent on how he will kill Larry if his statement is false but sincere. In this case, Oscar is free to kill Larry any way he chooses (although if Oscar decides to push Larry off the roof, Larry's prediction becomes true, and Oscar must also shoot him to fulfill his promise).
But we might also take that a prediction is an expression of personal belief, i.e., that when Larry says "You are going to push me off the roof", it should be understood as "I believe that you are going to push me off the roof". In this case, Larry's statement is honest if he does believe Oscar will push him off the roof, and a lie if Larry believes that he won't. Taken this way, Oscar can now evaluate Larry's statement in both relevant dimensions (true/false and sincere/lie), giving us four possible outcomes:
True and sincere prediction: Oscar must shoot Larry
False and sincere prediction: Oscar may kill Larry by any means he chooses
False and insincere prediction: Oscar must push Larry off the roof
True and insincere prediction: Oscar must shoot Larry and push him off the roof
Since Oscar can't know for sure whether Larry really believes in his stated prediction, his best course of action is to push him off the roof and shoot him, which fulfills Oscar's promise in every eventuality.
