KDx uses a subscription model, because of the nature of the technology, which fundamentally requires that it runs on a fully-configured web server.
The RELAY system in particular makes extensive use of back-end server technologies, and simply can not operate in any other way.
Even if lifetime license purchase option was available, you still would not be able to download the software and use it on your own computer in isolation from this website - it just doesn't work like that, nor can it ever.
For those who are worried that a subscription model means that you will lose access to the system if the service is ever discontinued, yes - that is true, but KDx does not store any of your data, so in the unlikely event that the service ends one day, you only would lose access to KDx, rather than any irreplacable data, as would be the case if services like Gmail or iCloud went down.
...and of course, if the service is unavailable, you don't pay for what you don't have.
If you want to use KDx occasionally, feel free to start and stop your subscription as you choose. You can cancel the renewal as soon as you subscribe, and keep using it for a month if you like.