Are airlines obliged to notify ticket cancellations due to no-shows?

I have had a long dispute with Lufthansa Airlines for 6 months now. The airline canceled the return ticket of a child in the 3 return tickets we bought (2 adults, 1 child). The child was already abroad so we didn't use the outbound ticket. The airline thus canceled the child return ticket with the "no show" argument (was not aware of this issue ahead of time).

From their policy

5.6. Please be advised that if you do not show up for any flight without advising us in advance, we may cancel your return or onward reservation.

The problem to all this is that the airline NEVER notified us of the cancellation. If we knew in time, we would have done something about it. Instead, we figured out when we already were at the airport for the inbound flight. Since the child was underage, my partner couldn't use her return ticket either since someone has to take care of the child.

Is there some law that protects us from this incident? I find it weird that an airline can do any alterations to a service without notifying you in any form.

(Some more info on our tickets as asked by commenter.)

Tickets were bought directly from the Lufthansa website. The itineraries were for UK-China via Germany. We got informed about this while trying to check-in at the Beijing airport in China. Notice that the previous day I tried to login in the Lufthansa webpage to check-in there but the page was buggy and I couldn't succeed to check our status.