re: Crackpot ASOIAF Theories SPOILERS

There were only about three sentences spoken in that exchange and Tyrion wasn't exactly in a frame of mind conducive of determining Tywins health. I don't look too far into Tyrions knowing of which room Tywin would be in, I think all the clues lie within the time period that Tywin was laying in state. If Tyrion knew Tywin had been poisoned we would know it as well