LH (and all IATA carriers) tickets expire at the end of one year. Thus, it sounds as though LH extended the tickets as far as they can be extended.
I would presume that as your wife is the primary caregiver that with proper documentation, your travel insurance will simply cover the cost of a new ticket.
Without knowing the routing and fare basis, it is hard to provide good advice as to whether asking for a compassionate refund is even useful.