Sure, active LD practice can increase your awareness, but I cannot see non-neglible result if you are already rising your sanity waterline with some CFAR-ish technics. If previous statement is false, then lucid dreamers are already more rational than general population. I haven't seen evidences for this hypotesis

It's important to note that only a small subset of lucid dreaming techniques are useful for rationality practice, as I mentioned in my first footnote.

For instance, the first method that I used to achieve lucid dreaming as a teenager was to flash blinking lights directly in front of my eyes while going to sleep. This allowed me to see a blinking pattern through my eyelids while sleeping, realize I was asleep, and hence achieve lucidity. While certainly effective at achieving lucid dreaming, this technique has no relevance to rationality at all.

Thus, I wouldn't expect lucid dreamers in general to be more rational than the general population. A person who sees lucid dreaming as their goal will select for certain things; a person who sees rationality as their goal and lucid dreaming as their tool will select for others.