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
Feel free to invest though, perhaps if you feel good about discarding hard drives on the moon I could interest you in space mirrors and for a low low price I'll lease you the spot where your harddrive lands for 100 years.
Okay, so here me out: the ultimate cold storage for someone like Iron Mountain. You'd have to understand that you'll need a minimum of 96 hours for retrieval time, and it's gonna be expensive to get that retrieval rocket there and back. Or, build a big dish and send the data via satellite signals.
You know what they say, 3-2-1 backup: three copies of your data, stored on two different types of media, with one copy kept offsite to guard against common-cause data loss. Depending on the cause, off-site could be a difficult place to go!
1) At the moment, we can't even get living people off the international space station let alone land on the moon and take off from the same spot twice.
2) If a space based proof of concept was practical, why would we not store our hard drive on the ISS. It is looking for some excuse to remain in operation and we can already come and go from it on a semi-regular basis?
3) If there was a global catastrophe to the extent that only moon based archives remained, then how are we going to go get them? This crisis destroys all data archives but preserves our space program?
4) Once we did get the drive back, what exactly might we do with it considering all other forms of data storage were destroyed?
5) If the data on the drive was so valuable that we were willing to pay millions of dollars for the chance that after Armageddon we could still get it back... Then why would the Chinese not just wait for us to place the drive then go get it themselves? Surely you would never encrypt it as the key would be just as vulnerable to loss as the data.