It seems like the participant since they have to proactively signal they’re in a lucid dreaming state with deliberate sweeping eye movements (LRLRLR) before answering questions.

It definitely matters because it implies we are consciously aware of ourselves during lucid dreaming but we’re asleep!. The memory of the dream is the only part that’s fragile. It’s another blow to the view that brain activity during REM is just randomly firing neurons rather than a creation of our consciousness.

FTA: “Our general approach was to awaken the participant from sleep after achieving successful two-way communication, in order to obtain a dream report. […] participants typically reported that they had received experimenters’ questions in their dreams”

⇒ If it was sunconscious, it did not stay that way.

Also, it would have been quite the subconscious. One of the participants decoded questions posed in Morse, and questions included simple math (“Then we presented a spoken math problem: 8 minus 6. Within 3 s, he responded with two left-right eye movements (LRLR) to signal the correct answer 2. The math problem was then repeated, and he again produced the correct answer”)