This would be a really great tip — I had no idea pressing the Mute button had any effect whatsoever — but when I do press it three times, I get options for A/V Reset, Auto Tuning, Set Top Box Power, and LG Remote Service. Interestingly, these are keyed to the colour buttons at the bottom of my remote, the only interface item I can think of with this feature.
But if I want to change the 'No Input' wallpaper(s), this three-press-mute seems not to be the answer. Intriguing, but not the answer we're looking for.