That has nothing to do with your optical drive or with this issue.
This is a Windows problem and has nothing to do with the firmware of your drive. You need to solve this problem first in order to update your drive.
Try uninstalling your controller driver and let Windows re-discover it on restart. Maybe that will solve your problem. Depending on your chipset, maybe there's an updated version of the chipset or storage drivers available, either from Dell or from Intel, nVidia, etc depending on which chipset you have. Updating your chipset drivers might solve the issue.
XD13 should work just fine with your drive. The reason it doesn't is because your drive is not properly installed in Windows and as such the LiteON updater can't see the drive.
Updating the firmware won't work until the drive is properly seen by Windows and the driver correctly installed, so you first need to solve your Windows driver issue/corruption problem and only then try to update the firmware. Your problem is a driver issue in Windows, and updating the drive's firmware alone won't solve it.