I have a Lenovo N22 Chromebook – Last year I tried to run the NoMachine Linux client on it via Crouton. It wasn’t very successful however Crouton has now been updated and the NoMachine client works very well. Using the Full screen keys it is possible to run the NoMachine client full screen. It has no impact on the Chrome installation. The only niggle is that you have to put the Chromebook in to developer mode and confirm you want to keep it that way on boot with Ctrl+d
This tells you what Crouton is and this is the Guide I used to do it. I used this option for the installation
sudo sh ~/Downloads/crouton -t xiwi,xfce
The N22 isn’t very powerful but with NoMachine and reasonable bandwidth I was able to watch full screen Kodi running on my remote i5 desktop and still be able to switch back and forth to the usual ChromeOS apps.