Well your computer shouldnt see the lite-on as it is right now, because the drive will not respond to the computer when the computer tries to find out what is connected, simply because there is no info on the drive.
If you have a sata drive in your computer, look at where it is plugged in on your motherboard, then go into iprep, and look at the devices it lists, and check the port of the drive. Then remember that, and plug your 360 drive into that port.
If you want you can use jungle flasher to do this aswell. Go to the dvdkey tab, make sure only use via ports is un checked, and browse through your port's until it shows a drive. Then remember that port number, and go to your motherboard, unplug that drive, and plug your 360 drive into it, then flash.
Here you can see ive found one of my burners with jungle flasher:
