A lucid dream does not fully simulate anything, it is an altered state that includes the subjective apprehension of verisimilitude. Perceptions and apprehensions, even outside of altered states, do not constitute proof of anything.

While I'm far from an expert on it... at best the dream simulations are still, extremely rudimentary. To the point that's usually how you can tell it isn't real by doing something like reading a book. IE it's largely believable, but only because you are put in a gullible state. Like watching 2 year old AI videos, while stoned.

People who are lucid dreaming simulate a full reality that’s nearly indistinguishable from the one they find themselves in during waking time.

You're not describing a simulation, you're describing a perception. A person perceives that they're seeing an indistinguishable reality, but we know that people's brains do not have the computational power to simulate molecular motion in even a cubic centimeter of air.

Or, if they look at the stars, are they then simulating an infinite space with infinite mass and all of the associated interactions inside of their finite brain? Of course not, that would be impossible.

Dreams are perceptions, not simulations.

I take issue with completeness in a very similar way. For example, imagine for some reason that in the simulation it’s impossible to think about penguins. Let’s say that penguins are so logically incomprehensible that we cannot implement this.

The implementation of the simulation could simply trap any attempt to think about penguins and replace it with something else. We would be none the wiser. The simulation still works even if there are states that we can’t get to or are undefined.

It could be that reality itself isn’t entirely complete and defined everywhere. Who’s to say this isn’t one big dream and that the sky isn’t there if we all stopped looking?

There is no escape from Plato‘s cave.