Has he tried resetting it to factory settings?
Before you rush off telling him its a panel problem it is also worth rulling out the software and other bits of hardware which supply the signal to the plasma panel.
In your picture the line isn't constant.
It would be worth doing a factory reset.
Then you need to find out how to get into the 'service menu' of the tv and do a more thorough reset - BE CAREFUL there are settings in there which you don't want to play with (unless you write down what they were before).
Then last option is to find a local approved LG repairer who could do a 'free quote'.
There are a number of plasma tv's which have known issues and manufacturers have been known to rectify for free to maintain good customer relations.