Shouldn't there be an automatic rebooking function that will automatically reobook you to the new flight. I have had a delayed flight and as soon as I went to the Kiosk and entered my PNR the new boarding pass with the new flight appeared and I could even change the seat assignment. On one instance I was bumped to First Class as no economy was available and I was number 1 in the line for being reaccomodated and the First Class passenger was a misconnect.
It only ended up being a 90 minute delay to the next flight. The gate agent of the original VCE flight should automatically send a command to the reservation system to offload you and rebook you on the next available flight or waitlist you or put you on another alliance carrier or in the worst case book you on an off alliance carrier.
You can access the Lufthansa website via the wifi onbaord and rebook you when you know that you will miss the next flight. Perhaps others are going to VCE from your flight and they may hold the VCE flight for 20 minutes or so and take you directly to the flight by bus or a car.
I would be in contact with the flight attendant who can relay it to the pilot who can then in turn talk with operations to see if they can hold your VCE flight or rebook you on the 11:05 AM flight.
Hope the OP makes it and we look forward to hearing from the OP. I know that Delta automatically rebooks you to the next flight if there are IRROPS as would other airlines and when you go to the kiosk or transfer counter your new boarding pass awaits. Your bags should automatically be transferred to the next flight and you can remind the transfer desk and gate agent to ensure that they reroute your bags to the flight you are booked on.