Hey there Tom. If you can't install the apk file, you need to enable your Android device to allow sources from outside the play store to install temporarily. I just tested the APK here on my android phone and it ran nicely :)
Thanks for your time and for trying Luna Lake!
Update:
If you're downloading a .bin file, try to changing your browser to Chrome. At least on my tests, Firefox for example, has a bug that pushes the file as Bin for you, not apk. Chrome gives you the file correctly. :D