Lufthansa charges for additional seat reservation after involuntary rebooking

I booked a flight through the Lufthansa website. The first leg from Frankfurt to Rome is operated by ITA Airways. The second leg from Rome to Accra is also operated by ITA Airways. The return flight goes from Accra to Rome, operated by ITA Airways, and Rome to Frankfurt, operated by Lufthansa. We booked for 2 adults and 1 baby. For the adult traveling with the baby (me), the seat reservation seems to be free of charge with ITA Airways. For the one Lufthansa flight, I had to pay for the seat reservation.

Now, two weeks after booking the flight, there was an involuntary rebooking. The first leg from Frankfurt to Rome, operated by ITA Airways, was canceled. As an alternative, the flight is now being operated by Lufthansa, but I am now expected to add and pay for an additional seat reservation. This increases the total booking price two weeks later without my consent, simply because the ITA Airways flight was unilaterally canceled. Is that even legal? After all, I booked everything through the Lufthansa website, they are my contractual partner and Lufthansa/ITA Airways belong to the same corporate group.