It lets me download it since it is in the play store, but it doesn’t let me buy it. Any ideas?
Some countries don’t allow paid apps.
Maybe try a VPN
just tried that with no luck. Same error message, it is about the country in Google Play, not where I am located. Weird thing is that if it were restricted for my country it wouldn’t even allow me to try to download it, there wouldn’t be any chance to buy in local currency either. 
You could try to buy Litchi from Amazon, this is also an Android version.
I managed to buy it from Google Play Stored logged in from the PC, not from the phone. Odd, but it worked at the end of the day. Litchi support replied: “Not our problem, talk to Google”.