My take on the "good luck" from Zazu is that the movie is from a different era with regards to how kids were punished and cartoon violence also. (Homer Simpson strangling Bart for example)
Simba was expecting a spanking -watch his little eyes widen in fear as he puts his tiny paw in his dad's massive paw print!! And he's just witnessed this guy give three hyenas a good thrashing.
Zazu doesn't know what Mufasa is thinking either, he probably knows that Mufasa would never hurt Simba but Mufasa is pretty angry and Simba will have to work hard to talk his way out of it.
Zazu has probably seen Mufasa angry before and thinks Simba is about to be either given a slap or verbally torn to bits.
He has no words for him, maybe he's a mixture of relieved the ordeal is over and in shock that cubs were almost eaten on his watch (even if it was unreasonable to expect a small bird to babysit two lion cubs!) He's weary and to top it all off now he has to escort Nala home in the gathering dark - coz that's safe!
So he wishes Simba the best and carries on his duties.