I would not bet on getting a flying job with LH in the foreseeable future. There are several 100s of fully trained license holders on the waiting list for a type rating. In fact, many have been "borrowed out" to other airlines like Austrian - while this is initially intended as a temporary measure, general opinion is that this may very well become permanent.
As a consequence, training activities at LH Flight Training appear to have (nearly) ground to a halt, and there is talk about LFT to possibly be merged with LXs flight school.
LH is set to get rid of the expensive pilots contract. The pool of pilots still flying under this contract is being dried out step by step; the main method for this is outsourcing of routes and aircraft to other airlines. VC (the LH pilots union) is battling this toe and nail, but general consensus seems to be that they are fighting a lost cause.
This was a short summary only and there is much expansion on this possible. But I will refrain from this for now and just say: If there is any other cadet scheme that seems open to You at the moment, focus on that one instead.