You’re correct on the first point but may have overlooked something on the second. LIghtBurn just uses libUSB which is builtin to Linux so doesn’t need to install any new driver.
Looks like the D1 uses a very common CH340 USB-Serial interface chip which should work fine in Linux. I know you had trouble with setting up LightBurn on Linux in another topic but there should be no reason this can’t be made to work. The biggest hurdle initially was making sure the firmware on the D1 was updated. Did you do this successfully from Windows?
If so, you should now be able to get this working in Linux if you’re up to trying it.
One key thing is you’ll need to make sure you give yourself permission to access the Serial ports which is documented in the LightBurn Linux installation instructions
sudo adduser $USER dialout && sudo adduser $USER tty
Without this the device may not appear or be available for communication.
Let us know how the Illustrator file plot develops.