Finally it worked. I was wrong. ADB is not required. It was my fault because I didn't understand how Livesuit tworks. Maybe others are confused as well so I explain what went wrong:
When entering the FEL Mode, Livesuit asks whether the device should be formatted or not as soon the device is connected to the PC. If you select YES Livesuit is immediatly flashing the image that was selected before (So it flashes the image under the path that is shown on the firmware Tab), no matter when the image was selected (Livesuit remembers the formerly selected image, even after livesuit was closed and started another day). So make sure, you select the correct image FIRST and AFTERWARDS enter the FEL mode or connect the device to PC. I assumed that I could enter the FEL mode and then select the image to flash...
Thanks for your help.