My experience is that when I'm working on training my capacity for sustained attention (which I do for a few months every few years), I frequently experience dreams in which I either start being critical of the dream-logic (thereby typically ending the dream), or have two simultaneous independent tracks of narrative, one of which follows dream logic and one of which doesn't. (For example, I will frequently have dreams in this state where I'm in a social setting and interacting with other people, where my interactions depend on not knowing certain things which I somehow know that I don't know. I've often tried to reproduce this dual-narrative state in my waking life, with no success.)

The relationship between this and LW-rationality is not clear to me. If I had to guess, I'd say they're related only by being in the same cluster of interests.