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Isn't this a solved problem? People have been living in the ISS for years.

The article mainly talks about temperature control but the other big reason to bury a lunar base is concerns about radiation. On Earth we have a big magnetic field to protect us from charged particles (like the helium-3 that ends up in lunar regolith) and an atmosphere to protect us from cosmic rays.

The ISS gets the full dose of cosmic rays being outside the atmosphere but those aren't that large a risk. For charged particles the ISS sits inside the inner Van Allen Belt which is the layer of charged particles that have been trapped by Earth's magnetic field. So astronauts are safe from all the high speed electrons and atomic nuclei that you'd have to endure during the day on the Moon's surface.

The Moon should grant a little more protection than the ISS since you can shovel regolith on top. As far as the raw radiation environment, it's about the same, in both cases half the sky is covered by a large planetary body.

The Earth's magnetic field gives no distinct advantage to radiation protection if you're already in a thin metal capsule.

The ISS experiences much shorter day-night cycles.

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