If the Moon is visible against a clear blue sky with a lux value of around 30,000 does it stand to reason that the lunar surface must be brighter than that?
It is better to use the unit of luminance, cd/m2.
Wikipedia gives examples of luminances:
2.5 kcd/m2 Moon surface;
5 kcd/m2 Typical photographic scene in full sunlight;
7 kcd/m2 Average clear sky;
10 kcd/m2 White illuminated cloud.
These values imply that the luminance of the moon surface is less than that of the clear sky, even though the moon is visible against the sky. The lunar highlands are clearly visible against the sky; the mare are less visible.
Surface brightness does not depend on distance, so in the photo below the brightness of the moon can be directly compared to that of the sky and terrestrial rock. No correction for distance is needed. Evidently, the brightness of the lunar highlands (albedo 0.2) is comparable to rock.
Photo from wikimedia commons