Capetonian, thanks for that. It does state on Lufthansa's FAQ's:
"If your flight is cancelled because of the airspace closure due to volcanic ash you may either claim a refund from Lufthansa or rebook free of charge to a later flight."
Rebooking was the problem. In theory a phone call or an email would have fixed it, but Lufthansa was unobtainable - not because of congestion, but simply because the systems were disconnected in anticipation of overload.
Rebooking could only be done by actually visiting a airport ticket desk (impractical) or booking a completely new ticket (expensive). Perhaps Lufthansa believes that the free-of-charge rebooking referred to above only applies if contact can be made to exchange the cancelled ticket for a new one - which was impossible.