The problem I had was not related to battery type. I was using alkaline AA. Instead the problem that occured was, I suppose, that the on/off switch on the AA battery case accidentally was switched off in the middle of an exposure. That locked the whole camera with mirror and blind and I had to have the camera serviced to get the locked state unblocked.I can't answer your question since I mostly use AA batteries. Be aware however, that the GX680 III doesn't like rechargeable batteries, so if you have used those, that might be the source of your problem.
So, I don't want that to happen again, that the AA battery case switch will move accidentally. I have a padded backpack without compartments and when I put the GX680 into the backpack I may accidentally move the loose AA battery case switch.
Not any more ....