On a normal Linux computer when someone says to log out and log back in it means Linux. Since you are running Linux inside a virtual machine on a Chromebook, you might get away with closing the terminal window and starting a new one. There is no login for LightBurn.
I know my way around Linux pretty well so hear are a few things to try and verify things are setup.
After you add your user to the dialout group, exit the terminal and start a new one then type “groups” to see if dialout is in the list of groups.
Next, without the USB plugged into the computer, power up your Ortur and then plug the USB cable into the Ortur and into the Chromebook.
Now type “dmesg” in the terminal window and look at the last few lines displayed. You should see something like “[75986.345200] cdc_acm 1-3.1.2:1.0: ttyACM0: USB ACM device”
Now type “ls -l /dev/ttyACM0” and you should see something like “crw-rw-rw- 1 root dialout 166, 0 Jan 8 19:17 /dev/ttyACM0”
These all validate the dialout group is being setup for the user and the Ortur device connection. You should then setup the /dev/ttyACM0 device in Ortur when you setup the device connection. Or whatever device name was shown on your system.
the device name, ttyACM0 in my case, is the device name you should see in your LightBurn Devices drop-down list.