The mainstream belief on this forum is that LH is rather reliable when it comes to luggage, compensates generously, and will deliver the bag as promptly as possible to you.
I share nothing but the latest point during my LH flying years. LH always was my record holder in loosing the bags, not once paid me a single cent for the delays and the missing bags ... but they always brought them back to me swiftly. Only once did I have to wait for more than 24 hours for the bag to arrive at my door.
So good luck with obtaining any form of compensation!