Is there a difference between fighting the hypothetical and recognizing that the hypothetical is badly defined and needs so much unpacking that it's not worth the effort? This falls into the latter category IMO.

"Negative impact on happiness" is far too broad a concept, "theism" is a huge cluster of ideas, and the idea of harm/benefit on different individuals over different timescales has to be part of the decision. Separating these out enough to even know what the choice you're facing is will likely render the excercise pointless.

My gut feel is that if this were unpacked enough to be a scenario that's well-defined enough to really consider, the conundrum would dissolve (or rather, it would be as complicated as the real world but not teach us anything about reality).

Short, speculative, personal answer: there may be individual cases where short-term lies are beneficial to the target in addition to the liar, but they are very unlikely to exist on any subject that has wide-ranging long-term decision impact.