My friend has Nexus 4 with a broken touchscreen. The display works though so in theory it's possible to use it with Ubuntu and an external mouse/keyboard.
But is it possible to install Ubuntu without ever touching the screen? Will external mouse work in Android? Will it help unlock the bootloader? Is there any way to unlock it from adb?
Update
According to this XDA page the unlock prompt can be used with hardware keys:
You will now be prompted with a warning message, use the volume keys to highlight Yes and select it using the power button.