Of course it is his job.
Lukaku has the luxury of the managers support and protection. He was able to put out appalling displays like the one against City and the non show against Liverpool (I think) but kept starting and playing through blips to eventually play himself into good form, confidence and stats.
Thing with Jose is, for me, he values discipline far too highly. It's good to have it but young players seldom do. He doesn't seem as enthusiastic about brilliant attacking skills as he does about discipline and all the stuff that come with experience. And more importantly, he seems unable to instill a high level of cohesion into our team. And that does not bode well for raw, exciting talents. All of this also explains Pogba strugglingunder Mourinho. His entire dogged hard working not-so- cohesive unit suits a Lukaku or Sanchez more.
It's just a shame really. One can't help but be envious of the coaching happening at our rivals right now. Unless your Sanchez or Lukaku I bet the players feel the same way.