As to your ultimate question, no there is close to zero chance that the German government will permit LH to become insolvent.
Hmmmm;
Condor was put into some kind of bankcruptcy protection proceeding last fall. That means the airline can still run flights, but court orders cannot be enforced anymore.
This game has been going on now for 6 months. Hence, EC261/2004 judgments cannot be enforced against DE.
A similar path could be reserved for Lufthansa.
Lufthansa may still run, but all claims cannot be enforced.