Before attempting this procedure make sure that you have this same controller on your system.
Open Device Manager and expand "Sound, video and game controllers"
Highlight the Line 6 device
At the top of Device Manager in the "View" menu select "Devices by connection"
This will show you a tree where your USB device is connected so you can find your USB Controller. For me the tree was:
ACPI x64-based PC
Microsoft ACPI-Compliant System
PCI Express Root Complex
Intel(R) USB 3.0 eXtensible Host Controller
The driver can be found at https://downloadcenter.intel.com/download/22824/Intel-USB-3-0-eXtensible-Host-Controller-Driver-for-Intel-8-9-100-Series-and-Intel-C220-C610-Chipset-Family
After extracting you will want to edit iusb3hub.inf and iusb3xhc.inf (located in \Drivers\Win7\x64 if you're on 64-bit) as follows:
Replace this text
[Manufacturer]
Intel(R) Corporation = Intel, NTAMD64.6.1, NTAMD64.6.2
[Intel.NTAMD64.6.2]
With this
[Manufacturer]
Intel(R) Corporation = Intel, NTAMD64.6.1
Then restart with the Disable Driver Signature Enforcement option (hold shift when selecting restart/Troubleshoot/Advanced Options/Startup Settings/Restart/Option 7)
Manually install the driver in device manager (right click Intel(R) USB 3.0 eXtensible Host Controller/Update driver/Browse my computer for driver software/Let me pick from a list of available drivers on my computer/Have Disk...)
Let us know how that goes or post your USB Controller if it's different.