In the end, Lapis didn't make them wait for long. When the sun had risen, she had already woke up; naturally, she didn't tell Rhode what had happened to her. While explaining the reason she fainted, she looked very panicked. Even she herself was also aware that she was unable to explain it properly, and besides saying sorry, she couldn't say anymore…
However, Rhode did not intend to spend much time on such a trivial matter. The most important reason was that they almost reached Unicorn Peak; no matter what kind of secret it was, Rhode was sure that he could find the answer once he arrived there.