So if I understand correctly, with the lid up you can get an image on the LG but with the lid closed you cannot? Is that correct? Yes, OS X is so clever that it stores two different user preferences for resolution under those conditions, e.g. lid up or lid down. But that means you can't change the lid up preference setting from the lid down state, or vice-versa. Sometimes OS X is too smart for its own good. 😟
One way to fix that is to use screen sharing between two Macs, assuming you have a second Mac at your disposal. From the second Mac, you can control the problem Mac, and change the resolution setting to one that works again with the LG while the MBP's lid is down.
Another solution is to start in Safe mode (hold down the Shift key through a restart) but there is a catch with this solution because the screen needs to be down. But there is no way to hold the Shift key down with the screen down. Hmm. One clever person on these forums folded up a piece of matchbook cover and placed it on the Shift key, hit the power button to start the MBP and then immediately closed the lid. That did the trick. The matchbook cover held the Shift key down. You can lift the lid once OS X finishes booting. You should be able to tell because the LG screen should be working under conditions of a Safe start.
Once the MBP is fully booted, with only the external screen active and the lid now lifted, go into Displays preferences and set the resolution to the one you have happily used for a year. Now you should be able to use the LG again with the lid down and not get that "Invalid Format" message.
A third solution would be to trash the preferences file com.apple.windowserver.plist and that should give a fresh start with the external display. Good luck whichever way you choose.
