This is not the right way to approach LH in these matters. I would write to LH in very short that you arrived at your final destination with a significant delay and request LH to pay compensation according to EC reg. 261/04 with reference that the delay of the incoming flight MUC-ORD flight was not extraordinary.

Be aware that it is almost 100% certain that initially your claim will be rejected. Then reply back maintaining the claim (unless LH has a very good reason for delay, i.e. the delay was extraordinary).