Well, the rules are very clear:
http://www.lufthansa.com/online/port...1818526&l=en#6
"For a Companion Ticket, the Miles & More member and the accompanying person (companion) must complete all travel together"
I know, they sometimes offer exceptions on a voluntary basis to this rule, but I have not seen any documents explaining the exceptions.
Edit: In the german forum
http://www.vielfliegertreff.de/miles...html#post73632
it is mentioned that "booking for both tickets has to be at the same time" and "in case case of cancellation both tickets have to be cancelled". So I think this also may apply for changes