mamak04 You may cancel and receive a full refund. It's article 5 of the EC261/2004 in combination with article 8. IANAL.
Thus, I think the legal situation is clear. In practice, I doubt LH will refund you unless you take them to court. My recent experience is they've been very accomodating with regards to rebookings. If rebooking to a different date is an option for your family, that might be the way to go (less hassle).