Your EC 261/2004 claim for delay compensation is made to the operating carrier of the flight causing the cancellation or delay. That is LH and LH is solely responsible. This applies however OP is ticketed and however he is rerouted.
The best time to do some digging as to the reason for the cancellation is at the departure airport. Ask staff. Typically they are not defensive about answering and sometimes may provide information you will not be able to dig up later.