I thought Omega was allowed to lie to sims.

He can certainly give them counterfactual 'realities'. It would seem that he should be assumed to at least provide counterfactual realities wherein information provided by the simulation's representation of Omega indicates that he is perfectly trustworthy.

Even if he's not, after he's given a $1m simulated reward, does he then have to keep up a simulated environment for the sim to actually spend the money?

No. But if for whatever reason the simulated environment persists it should be one that is consistent with Omega keeping his word. Or, if part of the specification of the problem or the declarations made by Omega directly pertain to claims about what He will do regarding simulation then he will implement that policy.