Few months back, my luggage did not arrive in DEL with LH (it was a fault of my initial flight on CO which was terribly delayed to FRA).
Anyways, LH DEL staff instantly gave me an overnight kit and 8000 Indian Rupees (roughly 200$ or less).
My luggage was then delivered in two days to me in MAA (which is where i wanted them to deliver it).

The LH DEL folks said the compensation was given because i was Star Gold via CO. I was simply glad to get any compensation on-the-spot.

The LH folks in DEL, BOM and MAA were all very helpful in general.