If you ask the questions without providing the limerick first, it never gets the right answer. When the LLM gets the wrong answer, it is usually because it reverts to its training data and gives a generic answer that doesn't apply to the limerick.
Why are you ruling out the possibility that training on the material may confer an advantage when the data is presented, even if the advantage may not be strong enough to pass the test without the data present in the context window?