Lufthansa IS doing their maintenance. This seems to be a part of the problem: Schedules and fleet procedures are made for airline operations and not for VVIP aircaft alternating between sitting idle for days and then be on tight schedules far away from their base in the media spotlight. I wonder why they did not schedule their brand new ACJ350 for long distance trips like this, but the oldest birds in the fleet? Those A340 are second hand Lufthansa aircraft converted to VVIP only later on.
What the RAF did was the smartest, most useful and flexible: Get some new MRTTs with a VIP interior.