If this may save time for someone with the same mobile, here is how you can make the Build & Run feature work in MMF2 with a Nexus 4.
The first time you plug your Nexus 4 with a USB cable, Windows installs a driver, but this driver doesn't support ADB (ADB is the tool of the Android SDK used by MMF2 to install the APK to the device). You can easily see it: when you click Build & Run in MMF2, MMF2 hangs, nothing happens on the Nexus and you have to kill the adb process so that MMF2 can continue working. Don't look at the LG web site, there is no driver for it. Fortunately there is a solution, the Google USB driver works with this mobile.
1. First, just in case you didn't do it yet, you have to activate the USB Debugging option on your phone. As the Nexus 4 runs Android 4.2, the developer options are hidden in the parameters. To activate them, open the parameters, click About this phone, and then click 7 times on the build number at the bottom of the list. It tells you "you are now a developer". Reopen the parameters, click Developer Options (around the end of the list) and then select USB Debugging.
2. Open the Android SDK Manager, open the Extras folder, select "Google USB driver" and then click the Install button. The Manager will download it to YourAndroidSDKFolder\extras\google\usb_driver.
Now open the Windows Control Panel, find the Device Manager and open it. In Other Devices (IIRC, or it could be also Android Devices) there is a "Nexus 4" entry. Right click on it, select "Update the driver", select "Look for a driver on my computer" (not sure about the exact text), enter the pathname of the Google USB driver in the Android SDK (YourAndroidSDKFolder\extras\google\usb_driver) and install it.
That's it, Build & Run now works in MMF2.
Note: for other Nexus devices like the ones made by Samsung and ASUS you have to get the driver from the manufacturer, don't use the one above.