If you purchase a nonrefundable ticket and miss the first half of the trip is it still...

I called the reservation department sent many emails to different offices. Was advised to call reservations after leaving a message on the feedback form. * Upon calling the reservations was informed that even though it was a mistake while booking on line I accidentally booked the same date for two tickets in two countries they said because of my ticket I could not cancel, change the date or be refunded. I have to travel as booked. I informed them it was impossible since I was departing one country on *nd and would arrive in Germany on the following day. The day after I am due to depart Germany as booked. Lufthansa leaves absolutely no room for that type of mistake.