No Refund for Lost Baggage from Lufthansa

I booked a flight from Istanbul to Montreal with a layover in Frankfurt on July 15th. I had a reservation near the Montreal airport as there were no bus or train connections to Ottawa in the evening. The real ordeal began when our delayed flight from Istanbul and a 1.5 to 2-hour wait on the tarmac in Frankfurt caused us to miss our connecting flight. Lufthansa informed us that the next available flight was with another airline the following day and arranged it for us. At the Lufthansa Service Center in Frankfurt, the staff assured us that our luggage would arrive safely and promised to compensate for the missed hotel reservation. Upon landing in Montreal, we discovered that our luggage was left in Frankfurt because the airline they arranged the flight with does not have a codeshare agreement. We have been waiting for our luggage for 6 days and have been continuously contacting Lufthansa for the payment of the missed hotel, but they keep denying our request, claiming it's not their fault. The staff at the Lufthansa Service Center gave us reassurances that everything would go smoothly, and we trusted their recommended flight. Lufthansa has been of no help in this matter, and our luggage is scattered in different countries. Lufthansa has not done anything right.