In the ZoT, there are 4 basic outcomes to the caster's queries, 2 for each version of Eloelle.
1) If Eloelle is an idiot and fails her save, she answers truthfully "I don't know." The caster knows this answer is truthful.
2) If Eloelle is an idiot and makes her save, she can answer truthfully "I don't know." or she can lie. But the caster will know she made her save and won't necessarily accept the given answer as truth.
3) If Eloelle is a genius and fails her save, she cannot answer "I don't know." She HAS to give the correct answer if she knows it regardless of the Patron's menacing whispers; the ZoT's caster knows this answer is truthful.
4) If Eloelle is an genius and makes her save, she can answer with a lie "I don't know." or she can tell the truth (though she might not, I'd her patron forbids it). But the caster will know she made her save and won't necessarily accept the given answer as truth.
Working with the stated initial premise that genius Eloelle knows the answers but lies about them, situation 3 raises an insoluble conflict between mechanics and the desired RP result. She can't both know the answer and not know it.