From what I read, it's hypothesized that this large cave that the Japanese discovered might be a lava tube. There is evidence of extensive lava flows on the Moon, so lava tube caves may (or may not) be expected too. Would cave formation be the same as it is on Earth in lunar temperature, atmospheric and gravity conditions? We are talking about extensive lava flows that produced the Moon's "seas", not just streams of lava emerging from Earth volcanos that produce tubes here on Earth. Much of the surface of the near side of the Moon seems to have been fluid at some time (or various times). I can imagine (science-fiction imagination is all it is) huge voids underneath the lunar "seas", created when the surface cooled and solidified over a hotter still-liquid layer that continued to flow. That wouldn't produce mere tubes, but extensive galleries miles wide.
If water ice has been found in shadows that never are illuminated by sunlight near the lunar poles, it might be even more likely in lava tubes that are always dark.
But... sadly my belief is that lava tubes are usually kind of featureless inside. Just rock tubes. That's how they appear here in California, at Lava Beds National Monument.
See here. They don't display the stalactites, stalagmites and the large crystals that one sometimes finds in limestone caves created by liquid water dissolving cavities in the rock, creating crystals by evaporation.