Interesting topic. I have a few points to add.

Lucid dreaming is a creative practice that taps new skills and sensations. In this way, it can be similar to meditation, learning a new language, learning to draw, or learning to write with your opposite hand. These activities tend to improve mental function by increasing neuroplasticity. But lucid dreaming isn't so special in this sense, as many other activities promote the same thing. Still, I think lucid dream can open up curiosity of other topics for more learning and neuroplasticity.

Lucid dreaming also increases time in REM through repetition and intent. Current scientific models of sleep emphasize that it's a period of recovery, with NREM mostly benefiting the body and REM mostly benefiting the mind. Spending more time in REM could plausibly allow for more mental recovery to improve alertness, learning, memory, etc. Here, it's not so much lucid dreaming but the side effect of more REM. On the other hand, too much REM is associated with depression.

Finally, as mentioned above, lucid dreaming is an opportunity to practice skills, similar to mental rehersal which is often used by athletes and musicians. I think though this is most effective when paired with real practice.