Hi there, I have Debian inside a ChromeOS and I've installed Lomiri.
From what I understand, Xephyr is needed to start a GUI and indeed it works with Lxde and KDE Plasma.
I used this script:
Xephyr -br -fullscreen -resizeable :20 &
sleep 5
DISPLAY=:20 startlxde &
[empty_row_here]
And run it. It simply worked with Lxde and Plasma.
I wonder if it's possible to change this script to make Lomiri start. 
I guess I might need to make it use Xwayland? And/or use the appropriate command where "startxlxde" is.