Searching for HYD-SHJ flights on the Lufthansa site doesnt yield results, nor does tracking the flight on Lufthansa. But the flight shows up on flightstats and other trackers.
Any clues as to why?
Like most airlines, Lufthansa follow a fixed numbering schema for their flights.
As per Wikipedia (in German), their current flight numbering schema, which they changed to in late 2010 includes :
LH8000 – LH8515 Flüge der Lufthansa Cargo
ie, Flight numbers between LH8000 and LH8515 are Flights for Lufthansa Cargo.
As your flight number calls within this range, it's obviously a cargo flight. Unlike many of their passenger flights, Lufthansa do not (publicly, at least) base cargo flight numbers on region, and thus this flight number could be used between any two locations.