Unlikely that there is anything to be done here, but OP might try all avenues just in case:
1. Write to LH and explain. Be apologetic, especially for not having notifying LH that they would skip the flight.
2. Look at all travel insurance possibilities. Likely any claim would be denied as undocumented, but stranger things have happened.
And, as others note, definitely make certain that if there are onward / return segments from FCO that those segments were not cancelled with the no show.