I’m surprised that there is no display adaptor shown in Device Manager. Then how is the external monitor working as there is only the one GPU (Graphics Processing Unit - display adaptor)? Did you also check in Device Manager > Other Devices (if listed) or Device Manager > View > Show hidden devices?
With the laptop turned on and a display showing on the external monitor, try shining a torch at an angle close to the laptop screen and check if there are any images to be seen. They will be very faint so trying this in a darkened room may help to see them if they are there.
If there are images:
then there is a backlight problem, either in the laptop LCD panel, LCD cable (video cable) or on the motherboard.
Usually with backlighting, the power for the backlights is supplied all the time to the LCD panel usually on pins 37-39 (if 40 pin connector otherwise pins 27-29 on a 30 pin connector) but not always, of the LCD cable (video cable) and they are turned on and off in the panel by a signal voltage sent on the backlight enable wire (BKL_EN) to the panel. The cable pin number for this wire can vary.
I can’t find a free schematic of the motherboard online but IF the motherboard’s board make and model number (printed on motherboard itself) is a Wistron LKM-1 WS 12291-2 then here’s a supplier that you can buy one from. If the motherboard is a different make and model search online for (insert motherboard make and model number) schematic to hopefully find it.
If there is backlight power voltage on the video cable on the motherboard you could always, turn off the laptop and disconnect the battery and using the hardware maintenance manual to access the video cable at the LCD panel, use an Ohmmeter to test the video cable wires for continuity from end to end to make sure that they’re all OK.
If the video cable tests OK then most probably the problem is in the LCD panel although you would need to check if the backlight enable wire has a voltage signal on it or not as it may be telling the backlights to turn off when they shouldn’t be (faulty lid switch sensor perhaps?). Otherwise the LCD panel will have to be replaced. Sometimes the Lenovo part number can be found on the back of the LCD panel itself to make it easier to find a replacement panel i.e. search for the part number ;-)
If there is no power on the video cable connector, having the motherboard schematics will help you to know the video cable pinout and also where the backlight power comes from on the motherboard
If there are no images:
then there is a problem with the motherboard from the GPU to the video cable connector as well as no backlight power on the motherboard. This may be difficult to find. What is the history of the laptop? Water damage, drop damage etc?
Hopefully this is of some help.