We don't know if the moon actually has any subterranean lava tubes, but if they do exist, a new analysis suggests they could be enormous.
Scientists at Purdue have crunched data from the GRAIL spacecraft that are mapping the Moon's gravitational field — and they argue that lava tubes on the moon are big big big. They have a conference paper about it here, and as they note in a Purdue press release:
"We found that if lunar lava tubes existed with a strong arched shape like those on Earth, they would be stable at sizes up to 5,000 meters, or several miles wide, on the moon," Blair said. "This wouldn't be possible on Earth, but gravity is much lower on the moon and lunar rock doesn't have to withstand the same weathering and erosion. In theory, huge lava tubes — big enough to easily house a city — could be structurally sound on the moon."
This makes me want to reread The Lotus Caves, a 1969 novel about two kids who discover a subterranean lunar world.