Mine actually had dust between the proximity sensor and the glass. The person at LG made sure the dirt wasn't there after replacing my LCD (for other reasons). I suggest you send it in for Warranty.
As a workaround, you can press the power button to end a call. You need to enable this...
Clean the glass above the proximity sensor. If you have a screen protector installed, remove it and see if the problem still occurs. If yes, it may be a hardware problem, or there's dirt trapped between proximity sensor and the glass.
I exactly had the same problem with less than a month old Nexus 4. Stock OS, not rooted. If I rotate the phone where the softkeys are near the camera/earpiece, they work. There's no touch no response on the area where the softkeys are supposed to be if you hold it in portrait mode.
Had the...