That doesn't sound right to me. If there's no air, then only black body radiation can be used to cool the data center. That means a massive radiator, a lot larger than a heat-to-air radiator+fan used on earth.
1. Put data on the moon
2. ???
3. Profit
For more info, check out their promotional video: https://www.lonestarlunar.com/video
I'd love to know how they plan to offset the cost of moving every single nut and bolt to the moon with... Cheaper cooling?
I mean, Microsoft experimented with sinking data centers under the ocean. That's certainly cheaper and more performant than shooting a rocket to the moon. That experiment ended. Why?