> no earthquakes
No but how about moon-quakes? Ok, not geologically active you say. But moon's been bombarded by asteroids it's surface is full of craters. Creating a crater wouldn't that be an equivalent of a moon-quake?
This is the correct answer. These lava tubes are, at their youngest, a couple billion years old. Since then, the moon has been thwacked very hard and -- on those timescales -- often. If the tubes haven't collapsed yet, then there's a high likelihood that they're exceptionally stable.
What about the sun's? If the force is strong enough to make earth orbit, and moon-to-sun distance oscillates, plus seasonal behaviour, there must be quite some straining tides...