From what you’re describing, it sounds like it’s the touchscreen display that has gone bad. If it were the audio unit, I don’t believe it would be rebooting. You can try the key first, but a used touchscreen is only $100 or so from eBay, so thankfully, not crazy expensive. The good news is that they’re plug and play, so find a decent one and try that. FYI, and screen, 2012-2016 will work. It doesn’t have to be specific to a 2012. The only other possibility I can think of is the Instrument cluster. The CANBUS runs from the IPC to the touchscreen…if you’ve developed some sort of issue there, then perhaps it’s causing the system to reset. That said, I haven’t really seen that before and I’ve seen plenty of failed touchscreens.
Just so you know, in the 2010/11 LR4’s, the audio unit controlled everything, in 2012+ models, it’s the touchscreen that controls all the other modules. That’s why I needed to know year model.