If Omega doesn’t simulate you, but uses other methods to gauge your reactions, he isn’t lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Suppose that Omega is known to be accurate with probability p1 for one-boxers and p2 for two-boxers. I.e. the odds are 1-p1 that a one boxer walks out empty-handed, and 1-p2 that a two-boxer gets $1001000. This information is public, so there are no lies. As p1 and p2 tend to certainty, would the unreliable predictor problem converge to the original one? If so, your point of simulated or hypothetical lying in the original problem is irrelevant.
Suppose that Omega is known to be accurate with probability p1 for one-boxers and p2 for two-boxers. I.e. the odds are 1-p1 that a one boxer walks out empty-handed, and 1-p2 that a two-boxer gets $1001000. This information is public, so there are no lies. As p1 and p2 tend to certainty, would the unreliable predictor problem converge to the original one? If so, your point of simulated or hypothetical lying in the original problem is irrelevant.