If you have a free account with Protonmail there aren't many options to use Protonmail on your Desktop. To do so you need to use the Protonmail Bridge which is only available for paid users. ElectronMail solves that problem (As well as for Tutanota).
To install Electron-Mail on KDE neon, go to the ElectronMail releases page and scroll down to version 3.2 which appears to be the latest prepackaged release for KDE neon. Download the package and install it by either opening it straight away with Discover or selecting it and Discover will open automatically.
After installing the package you can find it by searching for ElectronMail, or by navigating to Applications/Office, in the main menu.
Tips and Tricks
After opening ElectronMail for the first time it will ask you for a master password. I used Keepassx to make one and save it. Enter it twice and it will take you to the Settings page where you enter your account details.
There are some additional fields for two factor authentication but in my case I just had to enter my username and password. Voila, Protonmail on the desktop!